Eric J. Heller — Why You Hear What You Hear- An Experiential Approach to Sound, Music, and Psychoacoustics

1271 published claims from this book.

• A 1000 Hz tone in air has a wavelength of about one foot
• A 180-degree phase shift occurs crossing any isolated resonance
• A 1900 Chicago patent replicated the Javanese angklung without crediting it.
• A 34-cent tuning difference changes a chord’s identity and residue pitch
• A 40 dB 1000 Hz tone moves air atoms by only about one nanometer.
• A 670 tuning-fork apparatus was displayed at the 1876 Philadelphia Exposition.
• A baffle blocks sound-cancelling air flow and dramatically amplifies multipole sources
• A baffle prevents acoustic short-circuiting when it makes air travel farther
• A bare vibrating string is nearly inaudible without a soundboard
• A bare vibrating string is nearly silent without impedance-matched coupling
• A barely audible sound moves air only a few atoms’ width
• A bell lowers a tube’s cutoff frequency, easing high-frequency escape
• A bell suppresses high partials by radiation loss, not boosting them
• A bell’s perceived pitch is usually absent from its actual partials
• A bell’s sound 100 miles away is physically inaudible even with sail focusing
• A bowed string drives the bridge with a sawtooth waveform
• A bowed string moves as a traveling kink, discovered by Helmholtz.
• A chair’s clang is the sum of many discrete harmonic oscillator modes.
• A chorus can have definite pitch even when every singer is slightly off pitch
• A closed conical bore resonates like a tube open at both ends
• A closed narrow-end cone acts like a double-open cylinder giving all harmonics
• A combined waveform can produce a perceived pitch absent from its actual frequency components
• A cone must reverse pulse sign to match an open tube’s resonance period
• A cone’s apex turns what would be a wave node into an antinode
• A Connecticut town has heard unexplained booms since the 1600s
• A Connecticut town has produced unexplained booming sounds for over 350 years.
• A constriction at a pressure node slows air and lowers resonant frequency
• A convincing chorus emerges from 5 to 10 slightly pitch-shifted copies
• A craftsman without formal schooling rose to challenge Helmholtz’s authority.
• A cylindrical half-open tube missing all even partials produces the clarinet’s hollow tone
• A diaphragm loading the bridge drives the Stroh violin’s horn
• A discrete chain of beads approximates the continuous sine shape of an ideal string
• A discretized bead-and-filament string reproduces sound-wave behavior
• A driven coupled system shows two separate resonance peaks
• A driven tube emits at the drive frequency regardless of its own resonances
• A dumb sinusoidal drive self-sets its phase relative to the oscillator
• A finite-length burst yields a short-lived autocorrelation that vanishes beyond its duration
• A fipple tuned by a variable resonant cavity yields a wide pitch range
• A fixed-geometry trumpet can only play a natural harmonic series, not scales
• A formant is a locally strengthened cluster of adjacent harmonics
• A free jet generates periodic vortices without any resonator
• A free mass has impedance proportional to its mass and forcing frequency
• A good speaking trumpet makes a good ear trumpet with size adjustments
• A hammer deposits its energy based only on local deformations, before returning echoes.
• A Helmholtz resonator’s phase shift turns acoustic short-circuiting into constructive output
• A high-Q oscillator needs about Q oscillation cycles to reach steady state
• A horn amplifies sound without increasing diaphragm motion
• A horn equation quantifies how bell flare shapes resonance frequencies.
• A horn’s main benefit is source loading, not directional aiming.
• A huge variety of speech sounds can be made without vocal folds
• A hypothetical compound tuning fork illustrates how complex vibrations decompose into sine waves
• A jet’s natural instability produces noise unless vortices periodicize
• A kettle drum’s kettle functions as an acoustic baffle
• A mathematical error by Ohm distorted the theory of siren pitch
• A medium’s intrinsic acoustic impedance equals density times sound speed
• A membrane is the two-dimensional analog of a stretched string
• A mouthpiece raises impedance to match the lips to the air column, boosting power
• A mouthpiece’s phase shift compresses tube resonances into a playable harmonic series
• A moving medium shifts sound speed, and speed gradients bend waves by refraction
• A nearby wall doubles a source’s radiated power via reflected amplitude
• A nineteenth-century tone generator used 10 tuned forks to synthesize timbre
• A perceived pitch can exist with no partial at its own frequency.
• A physical impulse excites all frequencies equally in struck instruments
• A piano frame must withstand up to 60,000 pounds of string tension
• A piano soundboard conserves and recycles vibrational energy through repeated edge reflections
• A piano with dampers down can reproduce recognizable speech
• A piston’s radiation efficiency depends on size relative to wavelength, not absolute size
• A pitch can be heard even when only its higher harmonics are present
• A police whistle exploits beating to produce a tone well below its actual frequencies
• A power spectrum retains no phase information, so multiple signals share it
• A pulse inverts when reflecting off a fixed string end
• A pure audible tone’s only correlate is a single sinusoid
• A reflecting wall doubles total sound power output from any source
• A register hole suppresses odd harmonics while leaving even ones intact
• A resonance unsupported by cooperating upper harmonics produces a wobbly, unstable note
• A resonance’s strength depends on where you drive it, not just its frequency.
• A resonance’s strength depends on where you strike it, not on the mode alone
• A resonant tube captures and reradiates the near field, defeating acoustic short-circuiting
• A resonant violin bridge presents an impedance minimum, unlike wind instruments
• A resonator responds only to the matching Fourier component of a complex wave
• A returning echo creates power-spectrum peaks spaced by its inverse time
• A rigid wall raises the impedance of adjacent air cells
• A rising pitch can perceptually loop back to its start.
• A room’s acoustic character is captured by a single impulse response
• A row of trees can filter a voice to sound an octave higher
• A self-reinforcing kink seeds the Helmholtz wave while its twin is damped away
• A self-taught instrument maker became a central figure in acoustic science.
• A sharp impulse carries all frequencies at once and yields the full power spectrum.
• A short pop can still carry a recognizable resonant pitch
• A signal’s autocorrelation is a cosine sum over its sinusoidal partials.
• A silk merchant pioneered waveform-beating experiments in the 1830s
• A singer’s formant near 3 kHz lets trained voices cut through orchestra sound
• A single delayed sound repetition creates a perceived pitch even from white noise
• A single impedance mismatch in a chain splits energy into reflected and transmitted parts.
• A single neural autocorrelator may handle both pitch and localization
• A single recorded click can predict any sound’s behavior in a space
• A single slope measurement of dB decay directly yields the reverberation time
• A single tone can be dissonant with its own high harmonics
• A sinusoidal vocal fold wave would make speech impossible
• A slight irregularity in a siren’s hole spacing drops perceived pitch an octave
• A small piston still radiates sound because velocity is slightly in phase with force
• A small resonator at an instrument’s throat shapes its whole spectral envelope
• A sonic boom is many sound pulses arriving simultaneously
• A sound pulse passes an open pipe end unreflected when matching pressure exists outside
• A soundboard must avoid too-perfect impedance matching to not drain the strings
• A soundboard optimally transfers vibration without being too resonant itself
• A speaking horn’s distant source location distorts vowel-forming resonances
• A speaking-trumpet flare can boost lower frequencies when wall dissipation dominates resonance enhancement.
• A spherical implosion converts compression to rarefaction after passing through focus
• A string’s harmonic frequencies encode the Pythagorean length rule
• A string’s stiffness raises its higher-frequency modes above the ideal values
• A Stroh violin amplifies string vibrations via proximity resonance and horn color
• A struck membrane’s perceived pitch depends on suppressing inharmonic modes
• A struck point’s position determines which membrane modes are excited and how loudly.
• A sum of sinusoids is periodic only if their frequencies share a common divisor
• A sum of sinusoids takes the period of the slowest common component
• A system with N independent vibrating parts has N distinct normal modes
• A tapping bridge adds trumpet-like harmonics to a bowed monochord
• A tenfold intensity increase is perceived as only twice as loud
• A tenor’s singer’s formant appears as boosted energy between 2.4 and 3.5 kHz.
• A tensioned filament acts as a linear spring obeying Hooke’s law
• A theorem developed for heat flow revolutionized acoustics.
• A thin constriction at a pressure antinode leaves resonant frequency unchanged
• A thirteenth-century Arab scholar first explained source-loading amplification.
• A tiny extra mass ruins a string’s harmonic spacing and makes it sound sour
• A true difference tone is audible even from inharmonic partials separated by 200 Hz
• A trumpet mouthpiece’s Helmholtz popping frequency shapes the instrument’s playable spectrum
• A trumpet without a bell has stronger high partials than with one
• A trumpet’s bell beams high frequencies forward, changing timbre with direction of aim.
• A tube’s emitted frequencies come from the driving tone, not its own resonances
• A typical living room’s reverberation time rises at low frequencies, producing a boomy sound
• A vibrating body’s sound comes mostly from the attached soundboard, not the string
• A vibrating pane can convert conversation sound into modulated laser light
• A violin becomes a complete physics lab using only a smartphone and free software
• A violin string clamped between steel walls would radiate almost no sound
• A violin’s peak acoustic output is only about 6 milliwatts
• A violin’s transient response to changes distinguishes great instruments from mediocre ones
• A vocal tract constriction at the mouth forms a Helmholtz resonator
• A wall’s edge acts as a point source of diffracted sound
• A wartime siren reached 184 dB, instantly fatal to nearby listeners
• A wind instrument’s playability depends on how many of its harmonics align with resonances.
• A WWII defense siren reached 184 dB, instantly deadly at the throat
• A-weighting, the legal noise standard, rests on dated single-frequency measurements
• Accurate hearing cannot be acutely sensitive to the relative phase of partials.
• Acoustic reflections arise from impedance mismatches between neighboring medium cells
• Acoustic resonance enhancement is used to purify tones by suppressing contaminating frequencies.
• Acoustic resonances can be tuned to compensate for specific hearing loss profiles
• Acoustical simulations can now compute complete sound fields in buildings
• Acoustics remains an open field with room for new discoveries
• Acoustics research culture is unusually collegial compared to other fields
• Active noise cancellation applies superposition but tops out near 20 dB reduction
• Acute phase sensitivity would make sound perception unusable across locations.
• Adding a detuned copy of a voice makes it sound like a choir.
• Adding higher partials can drop the perceived pitch of a tone
• Adding mass at a node leaves that mode unchanged
• Adding mass to the bridge disrupts impedance matching and mutes the violin
• Adjacent compression and rarefaction regions can short-circuit and kill radiated sound
• Adjacent in-phase sound sources compound power as the square of their number
• Adjacent opposite-phase regions on a vibrating surface cancel their radiated sound
• Adjacent surface compressions and rarefactions can cancel sound before it radiates.
• After a supersonic object passes, its sound can still arrive from two locations simultaneously.
• After Q oscillations the amplitude falls to 4% and energy to 0.19% of original
• Air cells for sound simulation must be far smaller than the shortest wavelength
• Air in bottle necks behaves as a damped harmonic oscillator, not a molecule-by-molecule system
• Air is a seething low-density molecular gas with constant collisions
• Air molecules collide billions of times per second yet occupy little volume
• Air motion is usually caused by more massive objects set in motion.
• Air transmits sound efficiently because adjacent air cells are impedance matched
• Air-to-fluid impedance mismatch would reflect most sound energy without matching
• All acoustic impedances are ratios of force to velocity
• All resonance reduces to structure, drive, and in-phase response
• Alternating current through a thin conductor generates sound via thermal expansion
• Altissimo sax notes require a tuned vocal tract resonance just above the pitch.
• Amateur equipment can reproduce textbook acoustics measurements accurately
• Amplitude adjustment does not change a mode’s characteristic shape
• Amplitude does not affect the period of a sinusoidally vibrating object
• An air column driving the reed kills the sound by opening on rarefaction
• An ammonium-salt fertilizer pile explosion killed hundreds in 1921
• An edited acoustics reference can exceed encyclopedias as a primary source on many topics.
• An ever-growing list of necessary conditions makes real-world contact impossible
• An impulse determines the average power deliverable at any frequency interval
• An impulse response is itself an autocorrelation of the system
• An instrument’s identity is set by its unique recipe of frequency components
• An instrument’s opening attack largely determines its perceived timbre
• An instrument’s playability depends on many cooperating, accurately tuned resonances
• An instrument’s upper partial strength determines how dissonant the same interval sounds
• An open pipe end inverts a sound pulse’s sign via a reflected rarefaction
• An open pipe end only reflects sound when an impedance mismatch exists there
• An organ stop mimicking the human voice has existed since the 1500s
• An oscillating impulse response is itself an early echo, a confinement effect
• An uncredentialed instrument maker became acoustics’ most incisive researcher
• Annoying noise is context-dependent, so good regulations cap decibel increase over existing levels
• Anti-reflection coatings work by breaking impedance mismatch into graded steps
• Any echo-producing system inevitably exhibits frequency power fluctuations
• Any initial shape repeats periodically only if all modes are harmonic
• Any pipe diameter change causes partial sound reflection at the junction
• Any plucked string shape decomposes into sinusoidal standing-wave modes
• Any signal can be parsed into simpler component signals
• Any string shape decomposes into a combination of normal modes
• Applying independent vibrato to partials splits one complex tone into two perceived instruments
• Architectural designs can be tuned for speech versus music
• Aristotle described sound as a spread of air impulses
• Assemblies of coupled beads reveal how parts collectively produce universal oscillation patterns.
• Asymmetric board shapes reduce acoustical short-circuiting by unbalancing antinodal regions
• At resonance the displacement lags the drive by a quarter cycle
• Attaching a small vibrating source to a larger surface boosts loudness by 25 dB.
• Attaching mass to a string lowers odd harmonics and can trigger chaotic screech
• Audible resonance requires balancing energy confinement against energy leakage
• Auditory cortex layers divide pitch extraction from pattern synthesis
• Auditory feedback amplification occurs at hair cells, not in the brain
• Auditory frequency resolution follows relative change, not absolute Hz
• Auditory nerves fire directly in response to electrical current applied to the ear
• Auditory perception of the same physical sound varies between individuals
• Autocorrelation and power spectrum are Fourier transforms of each other via the Wiener-Khinchin theorem.
• Autocorrelation averages products across all shifted pairs
• Autocorrelation can recover hidden frequencies and amplitudes from a mixed signal.
• Autocorrelation discriminates echoes from genuine distinct sounds.
• Autocorrelation gives complex sounds a collective summary property, analogous to molecular mass and charge.
• Autocorrelation is mathematically equivalent to the power spectrum
• Autocorrelation magnitude reveals how long signal features persist
• Autocorrelation measures how a signal correlates with itself shifted in time
• Autocorrelation measures periodic self-similarity in a signal across time delays.
• Autocorrelation nearly perfectly predicts perceived residue pitch across a range of tone series.
• Autocorrelation predicts perceived pitch of non-harmonic partial groups
• Autocorrelation predicts pitch yet met lukewarm reception
• Autocorrelation, proposed in 1951, remains essential to pitch perception theory
• Autocorrelations are positive-coefficient cosine sums maximal at zero lag
• Averaged products of different-frequency cosines vanish, so only matching frequencies survive
• Basilar-membrane frequency sorting is too crude to explain our pitch discrimination
• Beat perception occurs even when partials go to separate ears, ruling out physical nonlinearity
• Beat rate is set by frequency difference, not by the true tone periodicity.
• Beating between two high-frequency tones can create a phantom low-frequency tone
• Beats per second alone cannot predict dissonance across the pitch range
• Beats transition to roughness to smoothness as partials separate on the basilar membrane.
• Being on resonance increases loudness even when energy is trapped inside
• Bell partials are unequally spaced yet still produce a definite perceived pitch
• Bending wave speed grows as the square root of frequency
• Blind listening tests cannot distinguish Strads from modern violins
• Blind people exploit repetition pitch to gauge distances
• Blind tests show little measurable superiority of famous old violins
• Blocking violin f-holes destroys the Helmholtz resonance and alters tone
• Body-volume changes drive the Helmholtz air mode in stringed instruments
• Boom-producing surface motion involves extreme acceleration but modest velocity
• Boosting an upper partial can shift perceived pitch toward that partial’s frequency.
• Boston Symphony Hall was the first designed with an acoustical consultant
• Bow stick-slip generates a sawtooth Helmholtz wave with rich harmonics
• Bowed strings sustain high harmonics indefinitely while plucked strings lose them quickly
• Bowing forces errant sharp violin partials into phase-locked even spacing.
• Bowing forces stiff-string partials into perfect harmonic alignment through phase-locked entrainment
• Brass players cannot hold off-resonance notes because lips form an interactive nonlinear drive
• Brass playing drives the lips above their natural vibration frequency.
• Breaking dipole symmetry adds a monopole component that dramatically increases sound output
• Breathing helium or SF6 should not change vocal-fold frequency, only the sound’s timbre.
• Bridge behavior must be studied together with the flexing top plate.
• Bridge resonance presents an impedance minimum, making it flute-like.
• Building balconies accidentally form corner retroreflectors that echo sound back to a speaker
• Buzzing lips generate many harmonics that resonance then shapes before radiating.
• Changing a component’s phase by 180 degrees is equivalent to subtracting that partial
• Changing internal gas density shifts the violin’s Helmholtz resonance frequency.
• Changing membrane tension during ringing produces a controlled pitch glide
• Chladni first recognized meteorites as extraterrestrial rather than volcanic
• Chladni lines mark where a vibrating surface is motionless.
• Chladni pioneered acoustics and identified meteorites as extraterrestrial in origin
• Chladni pioneered multimedia science presentation two centuries before PowerPoint
• Chladni plate vibration resisted mathematical solution even for Germain and Lagrange
• Chladni plate vibrations bridged science and mysticism around 1800.
• Chladni plates sing purely only when one mode alone is excited
• Chladni systematically catalogued vibrations of forks, bars, and rods beyond plates
• Church bells could realistically be heard 100 miles away on quiet water.
• Churches embedded damped Helmholtz resonators in their walls for centuries to absorb sound
• Circle-of-fifths tunings can be visualized as laser bounces inside a mirrored circle
• Claims that silencing inharmonic partials improve tone deserve experimental verification
• Clarinet bell suppresses tonehole back-reflections at short wavelengths
• Clergy and scholars fought priority disputes over the speaking trumpet’s invention
• Click pairs separated by small intervals are perceived as a distinct pitch
• Cochlear implants only help when the auditory nerve itself is intact.
• Cochlear implants raise word comprehension from zero to 70-90 percent with retraining
• Cochlear resonance and tonotopic pitch mapping were theorized as early as 1683
• Cochlear structures can be destroyed by invisible submicroscopic vibrations
• Coherent scattering among tightly packed molecules enables clear vision.
• Collisions with neighboring particles permanently lock expelled particles out of resonance, carving ring gaps.
• Comb-filter notches are far easier to detect on white noise than on music
• Combining modes with incommensurate frequencies yields ever-changing, nonperiodic motion
• Complex high-Q objects multiply echoes while each weakens
• Complex sound-emitting surfaces can be modeled as arrays of simple pistons
• Computer simulation can now reproduce everyday impact sounds convincingly
• Computers can modify pitch and formants independently of speech timing
• Concave curved walls confine whispers to travel tens of meters
• Concave sails focused distant bell sound onto a ship 100 miles away
• Conceptual confusion about sound reflection delayed its speed measurement for centuries
• Concert hall acoustic reputations often improve with age regardless of design merit.
• Concert hall power fluctuations are roughly 11 dB regardless of details.
• Concert hall sound varies 20-30 dB across frequencies yet listeners barely notice.
• Concert hall surfaces reflect low but scatter high frequency sound
• Concert orchestra layout favors right-ear treble but leaves treble physically on the left
• Confinement or wave return, not mere amplitude, is essential to resonance
• Confinement reflections amplify sources only when wave sign is preserved
• Confining a vibrating source makes it radiate louder sound
• Confining reflected sound can radiate more power than an open bell on resonance.
• Consonance is a continuous sensation while dissonance is an intermittent one
• Consonance is continuous tone flow while dissonance is intermittent roughness
• Constricting a tube at a pressure antinode leaves the frequency unchanged
• Constricting a tube’s open end transforms it into a Helmholtz resonator.
• Continued loud noise exposure can raise blood pressure and damage health
• Continuous-spectrum noises can carry pitch perceived from spectral peaks
• Correct free-edge boundary conditions for plates came only in 1850.
• Correct theories of pitch perception were suppressed by Helmholtz’s authority
• Correlograms track spike-train periodicity over time via sliding windows
• Coupled oscillator modes smoothly trade character as one natural frequency passes the other
• Coupled oscillators barely interact when their natural frequencies differ greatly
• Coupled oscillators trade energy back and forth, creating audible beating
• Coupled oscillators underpin most heard sound production
• Coupled string and board modes produce wavering sound rather than steady tone
• Coupled-oscillator energy sloshing causes the cello’s notorious wolf tone
• Coupled-oscillator intuition substitutes for impedance algebra in explaining reeds.
• Coupling a reeded air column to the vocal tract splits into two shifted modes.
• Cupping a hand over the ear boosts hearing via Helmholtz resonance
• Damper pedal and decay settings govern sympathetic vibration and note fade time
• Damping rates add directly while quality factors do not
• Deep-ocean pressure and temperature trade-offs create a sound-speed minimum waveguide
• Delayed loudspeakers preserve direct-sound localization in public venues.
• Delays under 100 ms are heard as timbre change rather than distinct echo
• Dense vegetation barely reduces highway noise below 2000 Hz
• Designing scales from upper harmonics yields ratios no Pythagorean scheme can reach
• Detuning a note’s multiple strings shifts its sound from warm to honky-tonk
• Difference and summation tones are perceived at arithmetic combinations of presented frequencies
• Different diameters tune Aeolian strings to activate at different wind speeds
• Digital audio must sample at least twice the highest frequency to capture it
• Digital audio’s only advantage is storage efficiency and robustness
• Digital copies are lossless while analog copies degrade with each use
• Digital sound gains only storage efficiency, since perception needs analog output
• Dipole sources amplify through near-field capture, phase shift, and reemission by a resonator
• Displacement rise time determines the sound frequency a quake produces.
• Displacing a tensioned string creates an unbalanced restoring force that drives oscillation.
• Dissonance arises from inconsistent stretch of notes versus partials
• Dissonance between complex tones reduces to summed penalties from near-coincident partials
• Dissonance depends on musical interval, not a fixed beat rate across frequencies
• Distinct tenor techniques enhance different harmonics to achieve the same projection effect
• Distinctly shaped sources yield identical far-field sound at the same frequency
• Double-kink string modes produce the octave via a center node
• Doubling a room’s dimensions doubles its reverberation time
• Doubling all pipe dimensions lowers its fundamental tone by an octave
• Doubling loudness needs ten times the violinists
• Doubling sound intensity raises the decibel level by exactly 3 dB
• Doubling sound wave amplitude quadruples the power delivered
• Downshifting all frequencies by a constant makes familiar music sound chime-like
• Driven resonator phase shifts 180 degrees across its resonance
• Driven systems oscillate at the drive frequency, not their natural frequency
• Driven systems settle to the drive frequency, responding weakly, not their natural one
• Driving a sounding board near a clamped edge produces antiresonance
• Driving point reveals whether a resonance peak is isolated or overlapping
• Driving-point independence reveals isolated resonances, while overlap makes vibration patterns location-dependent
• Drum membrane modes are not harmonically related
• Drummers hear different kettle drum tone than distant audiences do
• Dynamic loudspeakers convert current into motion via a coil driving a magnetized cone
• Each added perpendicular boundary halves the solid angle and adds a reflected acoustical image
• Each normal mode keeps its spatial shape while oscillating at one frequency
• Each piano string has two independent polarization modes doubling the coupled-mode count
• Ear trumpet bells need to match wavelength to capture low-frequency sound
• Eardrum damage requires hundreds of times the overpressure of an irritating sonic boom
• Earlier-arriving sound from a less loud source dominates perceived location.
• Early 20th-century hall design outperformed later modern acoustic engineering
• Early echoes determine the coarsest spectral shape of brass and flute instruments
• Early horn theories wrongly attributed amplification to wall vibration.
• Early reflected sound localizes sources while late sound becomes directionless
• Early reflections from nearby surfaces give performers essential auditory feedback
• Early strong versus late weak echoes dictate spectral fluctuation character
• Earthquakes deliver a sharp compression wave felt as a blow to the feet
• Echo interference creates sinusoidal power fluctuations that average to zero
• Echo time delay determines which frequency components get filtered out
• Echo timing and intensity alone can reconstruct a system’s full power spectrum
• Echo timing is used as an auditory distance cue by the visually impaired
• Echoes are the defining confinement mechanism behind all resonances.
• Echoes go unnoticed while unrelated simultaneous sounds are localized normally
• Echoes rearrange spectral energy without changing its total
• Echoes reshape but never change the total energy in a source spectrum
• Edge diffraction sources can be canceled by out-of-phase speakers
• Eighty singers and a duet are perceived as the same pitch
• Elastic recoil and momentum, not Bernoulli effect, mainly close the vocal folds
• Electronic enhancement can raise hall reverberation dramatically without audibly compromising speech or acting.
• Electrons in quantum corrals show acoustic-style resonance and antiresonance
• Electrons on surfaces behave like waves that can be confined by atomic structures
• Elliptical rooms focus whispered sound at the opposite focus
• Endlessly accelerating beat rhythms are Shepard tones shifted down in frequency.
• Energy lost per oscillation is proportional to remaining energy, producing exponential decay.
• Engineers combine connected parts into a single lumped system response
• Entrainment’s broad wind-speed range makes the Aeolian harp playable
• Environmental changes make each piano’s resonances unique and unstable
• Equal masses transfer energy completely while mismatched masses reflect some
• Equal temperament makes any piece transposable without changing tonal relations
• Equally spaced trees yield near-equal repetitive echoes ideal for notch suppression
• European musical scales are remarkably limited compared to other traditions.
• Evanescent waves confine sound to surfaces when step spacing is sub-wavelength
• Even anechoic rooms have a low-frequency operational limit
• Even everyday sounds like crinkling and creaking lack full mechanical explanations
• Even Mersenne, who first measured sound speed, rejected simultaneous string modes
• Even nonperiodic and arbitrary curves can be built exactly from sinusoids.
• Even percussive clang is a superposition of pure sinusoids
• Even the father of acoustics could not predict a hall’s sound before completion.
• Even the perfect octave is routinely violated in piano tuning
• Even very loud sounds move air by only about a micron.
• Every aspect of the physical universe is vibratory at some level
• Every level of the physical universe is vibrational or wavelike
• Every mode of an object’s vibration is itself a sinusoid
• Every periodic signal repeats at all integer multiples of its period
• Every wave mode is simultaneously an oscillator depending on viewpoint
• Every wave-like quantity has an uncertainty principle tying its Fourier transform pair
• Experienced players hear no difference from kettle drum vent holes
• Exponential profile alone does not fix horn length, leaving design freedom
• Extended light sources like planets scintillate less than point sources like stars
• Extra partials anchor complex-tone pitch against loudness-induced shift
• F-hole edges return chirped echoes that shape the violin’s broad frequency response
• Fan-shaped concert halls discourage early side reflections and tend to fail acoustically.
• Fan-shaped halls discourage early side reflections and tend to fail acoustically
• Fast air jets are inherently unstable and inevitably produce sound
• Fast wave propagation does not require fast motion of the medium itself.
• Faster sound decay produces broader spectral peaks, per the time-frequency uncertainty principle.
• Fechner’s logarithmic law and Weber’s ratio law are one and the same.
• Fechner’s logarithmic law is mathematically equivalent to Weber’s proportional-JND law
• Female voices are harder to lower than male voices are to raise
• Feynman’s freshman physics lectures remain treasured by experts decades later
• Feynman’s Lectures on Physics remains a canonical source for physics pedagogy
• Finite cosine sums can never yield decaying autocorrelations, forcing a smooth power spectrum.
• Finite signal duration sets a floor on achievable frequency resolution in a sonogram.
• Finite wire thickness raises higher piano partials, producing stretched harmonics
• Fixed vocal tract whistles hold pitch while cavity-free jets rise in pitch with airflow
• Flat rectangular rooms do not diffuse sound; slight wall curvature does
• Flat two-dimensional shapes can ring like bells when held by hand
• Flesh is a poor sound transducer because it damps vibration
• Flute resonances are impedance minima while trumpet resonances are impedance maxima
• Flute tone arises from jet instability locked to tube resonances
• For short wavelengths, walls only confine sound rather than amplify its power.
• Force and acceleration are in phase yet work requires force and velocity in phase
• Four centuries passed before Newton restated the proximity resonance effect
• Fourier analysis alone cannot explain perceived pitch of a tone
• Fourier analysis of echoes yields alternating strong and weak spectral bands
• Fourier analysis recovers constituent sinusoids from any summed waveform
• Fourier analysis’s mathematical elegance misled Ohm and Helmholtz
• Free edges reflect impulses with the same sign; clamped edges invert them.
• Frequency measured in Hertz is dimensionally inverse seconds
• Frequency perception requires logarithmic measure because octaves multiply by factors of two.
• Frequency response varies wildly across a hall yet listeners barely notice
• Frequency stays constant across media, so slow speed shortens wavelength
• Frequency-domain analysis may hide the very properties that make violins great
• Fricative consonants are produced by turbulent jets of air
• Friction acts like rent proportional to the energy an oscillator stores
• Friction always caps how much energy resonance can store.
• Friction extracts energy proportionally to the amount stored.
• Friction is a lumped label for energy dumping to outside systems.
• Galileo first conceived of and made permanent sound recordings
• Good wind instruments align tube resonances onto each partial of the drive note
• Greek theater resonators added reverberation-like effects without walls.
• Ground reflection colors all outdoor speech and creates comb-filter pitch
• Hair cell shearing opens ion channels via single-molecule tip links
• Hair cells are overdamped and cannot oscillate pendulously
• Half-period delay of a tone cancels odd partials and raises pitch an octave
• Harmonic content alone produces recognizable, describable timbre qualities
• Harmonic phases in wind instruments are fixed by pulse-driven resonance, not random.
• Harmonic spectra never occur exactly in real objects
• Harmonious orbital ratios are weeded out because they destabilize orbits
• Headphone reversal changes the sound pattern yet not what listeners report hearing
• Healthy ears emit sounds that are used to screen newborn hearing
• Hearing a pitch with no corresponding partial is perception, not auditory illusion
• Hearing detects pressure changes, not absolute ambient pressure
• Hearing is unique among senses in being partially restorable by a device
• Hearing relies on molecular tip links with no known repair mechanism
• Hearing transduces sound into nerve signals through fragile tip-link molecules with no repair mechanism.
• Hearing waveform beats disproves strict place theory of perception
• Hearing waveform envelope beats requires perceiving phase, not nonlinear distortion
• Hearing- damaging sound varies air pressure by only 0.001 percent
• Helium and sulfur hexafluoride change voice timbre, not pitch
• Helium voices sound high-pitched because formants shift, not because pitch changes
• Helmholtz air resonance extends violin support below its lowest body mode
• Helmholtz distinguished synthetic from analytic perception of sensations
• Helmholtz foresaw hearing mapped onto a mathematical frequency model like optics
• Helmholtz held that phantom tones are real distortions produced inside the ear.
• Helmholtz identified hair cells as the ear’s frequency-analyzing resonators
• Helmholtz never clearly separated perceived pitch from the presence of a matching physical partial
• Helmholtz resonance requires wavelengths far exceeding the vessel size so internal pressure stays constant.
• Helmholtz resonators amplify tones by exposing the eardrum to internal cavity pressure
• Helmholtz theorized thousands of basilar fibres act as tuned resonators
• Helmholtz wrongly assumed every heard pitch requires a physically present partial
• Helmholtz’s 1863 work originated most core concepts in musical acoustics
• Helmholtz’s 1885 roughness theory of dissonance still holds today
• Helmholtz’s double siren locked phase while filtering each siren to one harmonic.
• Helmholtz’s hand-computed dissonance curve matches modern algorithmic computation
• Helmholtz’s nonlinear-interaction theory of missing fundamentals is untenable
• Helmholtz’s resonance theory persisted for decades despite being flawed
• High-frequency drivers need far less motion than low-frequency drivers to radiate similar loudness.
• High-frequency forcing is resisted by mass while low-frequency forcing is resisted by spring stiffness
• High-frequency noise resists cancellation because its wavelength approaches headphone size
• High-frequency wave attenuation spreads out seismic displacement and lowers surface acceleration.
• High-Q resonances are problematic because they lock onto exact frequencies
• Higher drum modes self-compensate and leave kettle volume unchanged
• Higher modes of a lumped bead string are not equally spaced, ruining periodicity
• Higher partials dominate pitch because their sharper autocorrelation peaks win
• Higher Reynolds numbers yield broader, higher-frequency jet noise than lower ones
• Higher string modes vibrate faster because greater curvature raises restoring force
• Historical claims of talking and harmonizing echoes were debunked as folklore
• Home-made pipe resonators reproduce theoretical resonance frequencies closely
• Horn acoustics are reciprocal, working identically for source and listener
• Horn confinement amplifies siren output via proximity resonance.
• Horn confinement forces air bursts to do more acoustic work
• Horn loudspeakers amplify sound through proximity resonance in a narrow throat
• Horn throats boost output by constructive interference with the source
• Hull and aircraft design can reduce wakes and sonic booms by a third.
• Human hearing detects pressure changes of a few parts per billion
• Human hearing requires far more SPL to detect low-frequency tones than mid-range ones
• Human hearing spans over one billion in power from softest to painful.
• Human pitch discrimination far exceeds the ear’s filter resolution
• Humans can hear the sign (180-degree overall phase) of a waveform
• Huygens explained repetition pitch by equating echo spacing with musical interval timing in 1693
• Hybrid instruments need a dipole or quadrupole vibrator plus a nearby tuned resonator.
• Identical reverberation times can mask drastically different room sizes and acoustics
• Idiophones produce sound by vibrating the instrument itself, not strings or membranes.
• Impacting one coupled bead excites two incommensurate modes whose sum is non-periodic
• Impedance can peak or dip at resonance depending on measurement point
• Impedance equals applied force divided by attained velocity
• Impedance is force divided by velocity and measures a body’s response to force.
• Impedance is measurable by controlling either force or velocity
• Impedance is minimal on resonance
• Impedance is the ratio of force to velocity
• Impedance mismatch at the pharynx junction shapes spectra via early return echoes
• Impedance mismatch causes partial reflection of energy between unequal masses.
• Impedance rests on mass, stiffness, and friction as the three universal properties of matter
• Impedance theory was intuited centuries before its formal equations existed
• Impulse response and power spectrum are interchangeable representations of a linear system
• Impulse responses of real-world acoustic systems drive musical sound
• Impulse velocity response serves as a ready-made autocorrelation
• Impure sound sources can fake phantom tone effects
• In evenly matched systems, the roles of driving and driven swap as energy sloshes
• In pure modes spring force is ±90 degrees out of phase with velocity
• In-phase coupled resonators radiate four times the power of one resonator.
• Inconsistent octave stretching that leaves partials linear is jarringly unpleasant
• Increasing flow speed transforms pure periodic tones into noisy turbulence
• Increasing string tension raises the frequency of a single-bead oscillator
• Inharmonic partials make discretized strings sound sour despite adjustable tension
• Inharmonic strings would sound like chimes regardless of frets or fingering
• Insect wingbeat sounds are an unavoidable byproduct of vortex-based flight
• Instrument behavior emerges from a shared set of physical mechanisms
• Instrument design exploits impedance mismatches to create resonance and timbre
• Instrument timbre determines how dissonant the same two-note interval sounds
• Instrument wall material barely affects the tone a player hears
• Instrument wall material barely affects timbre; the air column determines the sound.
• Integer-multiple harmonics of a fundamental can generate a full scale
• Integer-ratio tugs from moons cause orbit wandering in rings
• Interaural timing alone cannot explain our sound localization ability
• Irrational frequency ratios make Lissajous curves rotate through all phase shapes
• Irregular frequency pairs still produce reliably periodic waveform beats
• Jet instability makes it easy for resonance to control vortex timing
• Jet instability makes some noise from fast air streams physically unavoidable
• Jet turbulence noise shifts from high to low frequencies as eddies decay downstream
• John Cage’s prepared piano realizes a coupled-string network instrument
• Just intonation rested on ideological mysticism about small integer ratios
• Kettle drum timbre shifts measurably with listener distance
• Koenig’s wave siren synthesized tones by varying air slit obstruction height.
• Large baffles suppress dipole short-circuiting but suit only a few notes
• Large radiating surfaces shift from quadratic to linear power gain with area
• Late design compromises like added seating can ruin a concert hall’s acoustics.
• Late-arriving room sound becomes omnidirectional and uniformly distributed
• Late-life cochlear implants can succeed even in people deaf from birth
• Later echoes refine the spectrum into sharper peaks limited by the echo delay
• Leaps of pure fifths fail to close because intervals and octaves are incommensurable.
• Linear superposition lets separate vibrations coexist independently while interfering in shared space
• Lip reeds adjust their behavior in response to reflected sound waves from the instrument.
• Lip vibration self-sustains through Bernoulli pressure and elastic recoil
• Lip whistling remains understudied despite decades of acoustic research
• Lip whistling stumped nineteenth-century acousticians as a causal puzzle
• Listener perception of voice pitch can contradict measured pitch
• Listeners hear tones that are absent from the presented sound
• Listeners perceive the fundamental frequency even when its lowest partials are absent
• Listeners reconstruct a perceived pitch that is not physically present
• Living upwind of a noise source materially reduces the noise you receive.
• Loading a source with a chamber is central to all musical instruments
• Logarithmic dB scaling makes measurement errors have modest effects on conclusions
• Logarithmic hearing means equal decibel steps need larger absolute pressure differences
• Logarithmic plotting makes the perfect fifth geometrically clumsy
• Logarithms are necessary to handle quantities spanning billions in range
• Long-lived instrument design features can outlive their original function
• Lord Rayleigh reported a woman’s voice echoing an octave higher from a fir plantation
• Losing a fixed percentage each period produces exponential decay.
• Loud audible tones require only tiny surface velocities of millimeters per second
• Loud bangs require surface accelerations exceeding one hundred times gravity.
• Loud brass notes form shock waves requiring precisely phased harmonics.
• Loudly driven brass columns self-organize into phase-locked shock waves.
• Loudness grows faster at low levels than Stevens’ power law predicts
• Loudness scales with frequency squared, requiring large amplitude at low frequencies
• Loudness slightly but measurably alters perceived pitch of tones
• Loudspeakers need enclosures to stop back-wave cancellation of sound
• Loudspeakers waste most amplifier power because sound conversion is highly inefficient
• Low diaphragm mass does not improve transient response in panels
• Low-frequency sound passes through ordinary walls because impedance shifts with frequency
• Lumped impedance treats pipe cross-sections as single units using volume velocity
• Luthiers’ tap testing is an informal impulse response measurement
• Mandarin speakers from birth develop perfect pitch at higher rates
• Many-part systems can behave coherently through normal modes
• Marimba is an idiophone coupling mechanical and air resonances through the NFC mechanism
• Marimba resonators amplify sound by capturing near-field energy that would otherwise short-circuit
• Marimba-like instruments with joined bars and resonators arose independently on three continents
• Masking acts within critical bandwidths, leaving distant-frequency sounds unaffected
• Mass dominates impedance at high frequencies, stiffness at low frequencies
• Mass, stiffness, and friction each dominate different frequency ranges
• Mass, stiffness, and friction each resist a distinct kinematic quantity
• Matched Helmholtz resonator sets enabled early Fourier analysis of sound
• Matching audio to a visual scene requires scene-appropriate impulse responses.
• Maximal power input occurs exactly at resonance and explains drive behavior
• Maximum sound output requires balancing radiation loss against internal friction
• Medieval church placement of sound vessels thwarted Vitruvius’s system
• Medium density and elasticity shape the pressure-velocity amplitude relation
• Membrane timbre depends on strike location and mallet choice
• Membrane wave speed equals the square root of tension over density
• Membranes of any shape lack harmonic spectra, unlike strings
• Mersenne first measured sound speed via echoes and speech timing
• Methane clathrate decomposition may explain mysterious Seneca Guns shoreline booms
• Micro-earthquakes far too small to feel can produce loud audible booms
• Microphones and loudspeakers are not reciprocal because their acoustic jobs differ fundamentally
• Microphones and loudspeakers are reversible transducers of pressure and electricity
• Middle ear bones amplify pressure over 30-fold via lever and area ratios.
• Minimal impedance horns must expand exponentially in diameter
• Minimum equipment sufficed to establish loudness decay as position-independent
• Mirror-and-light-beam amplification turns tiny vibrations into visible beat patterns on a distant wall
• Missing-fundamental pitch does not involve hearing an actual sinusoidal partial
• Mistuned musical partials produce slow timbre or quality beats distinct from loudness beats
• Mistuned voices destroy phase predictability and broaden perceived pitch
• Modulated light beams can generate sound from dark surfaces via heating
• Moisture, cracking, and tension drift make every grand piano uniquely voiced over its lifetime
• Moog patented removing every other upper partial to get brightness without raspiness
• More diffraction occurs for longer-wavelength, lower-frequency sound
• Most real sounds have autocorrelations that decay over time.
• Most vibrating objects produce inharmonic partials, unlike the ideal string
• Mouthpiece geometry permanently sculpts instrument tone via early echoes
• Moving formants and pitch can disguise voices while keeping speech intelligible
• Moving one’s head shifts spectral notches that encode source direction
• Moving the flute cork changes the spectrum far beyond mere length effects
• MP3 compression exploits psychoacoustic limits to shrink files tenfold with little audible loss
• Multiplying an autocorrelation by an analyzing cosine yields the power spectrum.
• Musical context and attack envelope shape chord pitch perception
• Musical instruments are engineered to suppress higher partials to avoid dissonance
• Musical notation omits harmonics that sonograms reveal
• Musical scales are exponential, so changing the octave needs logarithmic scaling
• Musical temperament directly connects to sound perception and natural vibrations.
• Musicians heard combination tones a century before physicists explained them
• Mutual resonance between sources boosts combined power beyond their sum
• Mysterious ‘cookie cutter’ sod displacements result from triggered shallow fault slips
• Naive resonance matching alone cannot explain Savart’s cup amplification.
• Napoleon recognized that irregular plate vibration patterns resist mathematical analysis
• Narrow time signals yield wide frequency spectra via beat cancellation
• Narrower pipes raise acoustic impedance through in-phase wall reflections
• NASA’s 1960s Oklahoma City sonic boom tests killed the US SST program.
• Nasal cavities function as a branched second passage shaping voice timbre
• Natural and urban noise has a broad, smooth power spectrum.
• Natural inharmonicity makes partial phases cycle continuously, so the ear ignores them
• Natural measurements correlate over time because dynamics persist
• Near-field versus far-field acoustics change which partials a listener hears
• Near-resonant coupled oscillators mix their motion into two equal hybrid modes
• Nearby reflecting surfaces constructively pile up wave reflections to amplify sound
• Nearby reflective surfaces can load a source and boost its output
• Nearby walls amplify monopole but not dipole sound sources
• Nearly all sound energy is reflected at the air-water interface
• Neckless Helmholtz resonators use near-opening air as their oscillating mass to reduce friction
• Negative echoes suppress power near zero frequency, creating missing spectral peaks
• Negative-magnitude microquakes generate audible surface pops
• Neural feedback restores sharp frequency resolution that hair cells lack on their own
• Newton explained tube amplification via repeated reinforcing motion
• No musical tuning system can be proven superior to another
• No perfect tuning system exists; all musical temperaments are compromised
• No pure integer-ratio system can tune musical intervals without compromise.
• No trumpet is built that plays in tune for all fingerings
• Nodal patterns for irregular plate shapes remain unsolved today.
• Node force balance determines tensions in a tensioned string network
• Nodes are stationary points where a vibrating mode has no motion
• Noise is best defined as unintended or accidental sound rather than aperiodic sound
• Non-sinusoidal sources still produce audible sinusoidal partials.
• Nonlinear vibrating systems generate sum, difference, and combination frequencies
• Nonperiodic sounds like chimes also decompose into pure sinusoidal partials, just inharmonically spaced.
• Objects vibrate sinusoidally when restoring force is proportional to displacement
• Objects vibrating at small amplitudes move sinusoidally, one sine per frequency
• Objects’ vibration mostly dies to internal friction, not emitted sound
• Ocarina pitch depends on total opening area, not hole placement
• Occupied audiences absorb up to 90 percent of incident sound in a hall
• Ocean depth creates a wave-guiding sound speed minimum around 800 meters
• Ocean temperature can be mapped remotely using sound propagation timing
• Oersted slid into vibratory pseudoscience after seeing Chladni’s patterns.
• Off-pitch choral singers still yield a definite collective pitch
• Offsetting siren hole rows shifts perceived pitch by changing periodicity
• Ohm’s law claims tone quality arises from combinations of simple tones
• Ohm’s mathematical error inflated the siren’s fundamental partial strength.
• On resonance, releasing sound reduces its loudness
• One instrument can sound like two notes by weighting partials within a shared series
• One of the two initial kinks seeds and reinforces the Helmholtz mode.
• Only a pure sinusoid comprises exactly one frequency.
• Only a sinusoid has a single frequency; every other shape contains multiple frequencies
• Only about 4% of bowing energy becomes audible sound
• Only accelerating surfaces, not steadily moving ones, generate airborne sound.
• Only an infinitesimal piston does no acoustic work at all
• Only one of four coupled-oscillator modes sounds a blown-closed reed
• Only pure sinusoids produce the sensation of a colorless tone.
• Only the (0,1) kettle drum mode changes internal air pressure
• Only the first row of trees produces significant echo reflections
• Only tones with periods in the 20-20,000 Hz range count as audioperiodic to listeners.
• Only trained, prompted ears can parse sound into individual partials
• Open geometries yield only low-Q resonances because pulses escape permanently
• Open reeds must vibrate below the air column’s playing frequency to be stable.
• Open tube ends preferentially transmit high frequencies and reflect low ones, smearing echoes.
• Open-tube end reflection arises from air-parcel overshoot into lower impedance beyond the opening.
• Opening toneholes raises pitch by marking where the tube effectively ends
• Opposite-phase monopole sources cancel at a distance when separated by less than a wavelength
• Oppositely phased paired resonators short-circuit radiation and raise Q to 70
• Oppositely phased resonators short-circuit each other and prolong sound decay.
• Optimal impedance matching uses geometric mean intermediate steps
• Ordinary listening blends analytic and synthetic modes simultaneously
• Organ pipes’ timbre arises from resonances cooperating with edge tone
• Orthogonal harmonic vibrations trace closed Lissajous curves revealing component motion
• Our brains subconsciously discount reverberation unless the sound is reversed
• Out-of-phase coupled motion stiffens a system while in-phase motion softens it
• Out-of-phase dipole cancellation strengthens as source spacing drops below a wavelength.
• Out-of-phase stereo speakers suffer reduced bass from acoustic short-circuiting.
• Out-of-tune upper harmonics and pure harmonic vibration produce the Aeolian harp’s eerie timbre
• Outer ear canal resonance explains peak sensitivity near 4 kHz
• Outer hair cells actively amplify and sharpen frequency response without signaling the brain.
• Outer hair cells actively amplify and sharpen sound before inner hair cells fire
• Over-confining sound in resonators can backfire through internal dissipation.
• Overlapping damped modes sound smooth while isolated modes produce terrible wavering
• Overlapping narrow resonances in dense spectra reveal wave dynamics
• Painted brick absorbs only about 1% of incident sound while wood absorbs about 15%
• Pairs of tones with irrational frequency ratios never exactly repeat their combined shape.
• Paper riders on a string predated Chladni’s sand as a nodal-line visualization.
• Partial spacing determines whether coincidences cause beating, roughness, or fusion
• Passive cavity resonance can amplify a drive without altering its motion
• Passive devices and even walls can amplify sound without power
• Pendulum period is independent of the bob’s mass even when mass differs a hundredfold
• Pendulum period is only approximately amplitude-independent for small swings
• Perceived beat rate equals the frequency difference, not true waveform periodicity.
• Perceived dissonance resists full quantification because it is a human impression
• Perceived frequency differences scale logarithmically, not linearly with Hz
• Perceived loudness falls off with distance more slowly than physical intensity does
• Perceived loudness integrates sound over a roughly one-second running window
• Perceived pitch depends on a note’s individual overtone amplitudes
• Perceived pitch depends on listening context, not just the physical spectrum present.
• Perceived pitch extends continuously down to a few hertz as pulse counting
• Perceived pitch persists even when the matching frequency partial is absent
• Perceived timbre depends on partial amplitudes but not their phases
• Perception cannot be proportional to stimulus across its full range.
• Perception of changing sound requires simultaneous time and frequency resolution
• Perfect audio reproduction only requires recreating the exact waveform at each eardrum
• Perfect impedance matching at the lips would ruin vowel fidelity
• Perfect pitch makes transposed tunes feel as wrong as odd colors do
• Perfect pitch works by matching autocorrelation peaks between heard sound and remembered notes
• Perfectly hard-walled halls would produce unbearably long echoes needing leaks to tame
• Perfectly synchronized voices are acoustically indistinguishable from one voice
• Periodic pressure waves are perceived as pitched while nonperiodic ones are not
• Phantom tone perception varies widely between individual listeners
• Phantom tones are heard as real pitches though physically absent
• Phase drift among coupled strings extends piano note sustain by reducing bridge power flow
• Phase relationships among source components shape far-field radiation directionality
• Phase relationships between subcomponents shape a source’s radiation pattern
• Phase shifting shared partials inadvertently alters amplitude through interference
• Phase-shifted air motion through f-holes reinforces sound radiation at high frequencies
• Philharmonic Hall’s acoustics resisted all fixes and remain imperfect decades later.
• Physical sound absorption can be strong enough to measurably alter room reverberation
• Physical wave experiments confirm ray tracing and numerical simulation predictions
• Physically correct octaves actually cause audible beats in a real piano
• Physically modeled synthesis can adjust piano characteristics without resampling
• Physically modeling sound sources enables flexible digital instruments
• Physicists have long dismissed pitch perception effects as anomalies
• Physicists have sometimes imposed favorite theories onto the ear
• Piano hammers strike strings at a point avoiding all low-partial nodes
• Piano strings and soundboards can exchange energy producing audible loudness shimmer
• Piano tuning must sacrifice perfect octaves to avoid beating against sharp harmonics
• Piano tuning stretched so far it has become a required sound
• Pianos are stretch-tuned so low notes sit flat and high notes sharp
• Pianos use multiple strings per note to improve energy transfer and loudness
• Pinning a node makes higher modes act as fundamentals of shorter strings
• Pipe diameter changes reflect pressure pulses with opposite sign
• Piston sound power scales with area squared, not linearly with area
• Pitch and phantom tones are independent because pitch needs no tone at its frequency
• Pitch can be heard even when no sound component exists at that frequency
• Pitch can be perceived even when no partial exists at that frequency
• Pitch can exist with no tone heard at that frequency, unlike phantom tones
• Pitch is a human synthesis keyed to autocorrelation, not pure physics
• Pitch is perceived logarithmically so the keyboard maps log-frequency to linear distance
• Pitch maps directly to the spacing of vibrations etched in matter
• Pitch of periodic sounds is determinable from the waveform’s cycle period
• Pitch perception codes operate in parallel and can compensate for each other’s loss
• Pitch perception corresponds to peaks in the autocorrelation function
• Pitch presence is defined by listener perception, not by acoustic analysis
• Pitch resolution exceeds smeared bandwidth via peak-locating algorithms
• Pitch standards varied by four semitones before the tuning fork standardized them
• Pitch switches to the higher frequency only when spacing is nearly perfect
• Pitch theories neglecting amplitude information cannot fully explain perception
• Planetary orbits avoid exact integer ratios because resonance causes instability
• Plate vibration solutions require proper edge boundary conditions, unresolved until Kirchhoff in 1850.
• Playing wind instruments louder shifts spectral energy toward higher harmonics.
• Plucked strings vibrate as a sum of harmonic partials, not as a pure tone
• Portable recording devices debunked extravagant echo claims
• Ported speaker enclosures exploit the 180-degree phase shift at resonance.
• Position and velocity are Fourier transform pairs, hence obey an uncertainty principle
• Power fluctuations persist because echo arrival times unevenly populate Fourier components
• Power fluctuations persist even where resonances overlap completely
• Power quadruples when amplitude doubles, since power scales with amplitude squared
• Power spectra capture component amplitudes but discard phase information
• Pre-computer acoustics could not test designs before construction.
• Precise tuning forks revealed auditory phenomena digital tools still struggle to match
• Pressure gradients drive air flow that cancels out multipole sound
• Properly timed small impulses can drive a massive system to immense momentum
• Properly timed small impulses can overpower far larger forces through resonance
• Proximity resonance in gramophones is the same gatekeeper effect as trumpet mouthpieces
• Proximity to a resonator suppresses, rather than amplifies, monopole sound sources
• Pulling the vocal tract resonance down bends notes but is self-limiting.
• Pure perfect fifths never close the octave, leaving a 24-cent Pythagorean comma gap.
• Pythagoras linked musical consonance to small-number string ratios by 600 BCE.
• Pythagoras’ simple-ratio tuning system proved ultimately unsatisfactory.
• Pythagorean tuning generates all notes from factors 3 and 2 alone.
• Pythagorean tuning generates scales purely from whole-number ratios of the fifth
• Pythagorean whole-number ratios led to the doctrine of the music of the spheres
• Q equals the oscillation periods needed to reduce amplitude by a factor of 25.
• Quantum corrals have cavity Q of 2 or 3, like a dead acoustic room
• Radiated sound depends on source area and air-displacement pattern, not just amplitude
• Radiation angle depends on surface wave speed via s equals c over cosθ
• Radiation losses are negligible compared to wall losses in narrow pipes
• Railsback chart quantifies the gap between stretched piano tuning and equal temperament
• Railsback curve shape follows bass and treble string construction limits
• Random media variations focus waves into high-energy branches without any lens
• Rapid beating between nearby partials causes perceived dissonance
• Rare events justify mechanisms requiring many precise conditions
• Ray tracing fails except on very abrupt or very gradual impedance changes.
• Rayleigh attributed a forest echo’s octave rise to size-dependent scattering of high frequencies
• Rays are surrogates traveling perpendicular to wavefronts.
• Reactive forces do no acoustic work; only the dissipative component radiates sound
• Real short bursts have continuous spectra needing Fourier analysis, not finite cosines.
• Real signals contain smooth distributions of infinite frequencies
• Real strings show slightly sharp partials because tight curvature stiffens them like bars
• Real strings’ slightly mistuned partials are a loved feature, not a flaw.
• Real tongue constrictions of finite extent alter resonances differently from idealized thin walls.
• Real-world acoustic mysteries range from sonic booms to whale communication
• Realistic periodic sound sources generate many harmonics, not single frequencies.
• Recognizing the sinusoid’s primacy founded modern acoustics in the 1800s
• Recording fidelity matters less than room acoustics and head movement for perceived liveness
• Rectangular rooms fail to randomize sound directions, violating Sabine theory
• Reed instruments divide into high-impedance and interactive pressure-valve subclasses.
• Reed instruments work as two coupled oscillators, reed and air column
• Reed opening at high mouth pressure amplifies the air column resonance by constructive interference
• Reed vibration frequency depends on reed, air column, and coupling
• Reeds must vibrate faster than the air column to reinforce resonance
• Reflected sound waves interfere with direct waves to create frequency peaks and dips
• Reflected sound waves pull a lip-reed player’s notes into resonance grooves, resisting off-resonance tones.
• Reflected waves’ timing pulls a reed’s buzzing frequency toward the tube’s resonance
• Reflecting surfaces can extract wasted energy from an inefficient sound source.
• Reflecting surfaces cannot create new frequencies in ordinary echoes
• Reflecting surfaces within an eighth wavelength amplify a source via proximity resonance
• Reflecting walls are equivalent to mirror-image virtual sound sources
• Reflections cannot introduce frequencies not present in the original sound
• Reflections from a nearby hard wall can double the sound amplitude toward the listener
• Reflections serve as spatial orientation cues for humans
• Refraction bends waves toward the medium with slower speed
• Refraction, unlike wall diffraction, can create near-total acoustic silent zones.
• Refractive index in optics is impedance, and mismatches cause reflection at interfaces.
• Register holes force overblowing by stripping the fundamental of its harmonic support
• Relative pitch perception is more limited than commonly assumed
• Removing a trumpet bell empirically strengthens the high partials above 1500Hz
• Removing every other upper partial yields brightness without self-dissonance
• Removing inharmonic 7th, 11th, and 13th partials fails to improve tonal quality
• Removing the soundpost makes a violin sound like a guitar
• Renowned violinists cannot reliably distinguish Stradivarius violins from modern ones by listening
• Repetition pitch equals the reciprocal of the echo delay time
• Repetition pitch falls then rises, unlike the always-falling Doppler effect
• Repetition pitch is computable by pure geometry of direct and bounce paths
• Repetition pitch requires standing on a large hard surface to get ground bounce
• Residue pitch is a designed perceptual process rather than a mere illusion
• Residue pitch is an event tone signifying repetitive beat occurrence
• Residue-pitch calculation from spare partial data recovers a bell’s perceived pitch
• Resonance arises when echo round-trip time equals an integer number of wave periods.
• Resonance energy storage alone cannot explain a brass instrument’s loudness
• Resonance is one universal phenomenon across all wave types involving structure, drive, and phase
• Resonance is universal constructive addition of force-driven velocity
• Resonance lowers impedance dramatically at an oscillator’s natural frequency
• Resonance maximizes driven power only at the cost of heating.
• Resonance maximizes the power a driving force delivers to a system
• Resonance occurs when the driving force and velocity align in phase
• Resonance occurs where impedance vanishes, yielding huge response
• Resonance peak height scales with the strength of the returning echo amplitude
• Resonance peaks always require compensating anti-resonant valleys in the spectrum
• Resonance peaks are always balanced by anti-resonant valleys nearby
• Resonance requires confined old amplitude returning in phase with fresh drive amplitude
• Resonance requires confinement of previously emitted amplitude
• Resonance requires old amplitude to add constructively with new drive
• Resonance requires round-trip reflections arriving in phase with the source
• Resonances compete for power as a zero-sum game when crowded together.
• Resonant confinement can backfire when internal dissipation exceeds radiation loss
• Resonant power dissipation actually grows when damping decreases
• Resonant reflections raise impedance in throats and reproducers
• Resonantly enhancing one high partial produces a perceptually separate note
• Resonator pitch scales with gas speed, volume, neck geometry
• Resonators amplify quiet near-field vibrations far more than direct air-column strikes.
• Resonators amplify sound by capturing near-field energy and reradiating it with a phase shift
• Reverberant sound decays exponentially because wall absorption removes a fixed fraction of remaining energy
• Reverberation time T60 measures how long sound takes to decay a millionfold
• Reynolds published the governing dimensionless number for vortex flow in 1883.
• Rich complex tones can contain internally dissonant partials without sounding dissonant
• Rich tones always compound internal and cross-tone dissonance
• Room acoustics extends pipe-mode analysis to many directions
• Room low-frequency resonances make expensive audio systems sound muddy or boomy
• Room mode density rising smoothly with frequency signals good acoustics
• Room resonances above 200 Hz overlap heavily, forcing isolated modes below that threshold
• Room resonances necessarily overlap because high Q would ruin intelligibility
• Room resonances shift from isolated to overlapping at the Schroeder frequency
• Room sound becomes uniformly diffuse over time
• Room sound homogeneous decay holds for typical rooms but can be engineered away
• Rotating hole patterns convert air puffs into precisely determined complex tones
• Rotating siren holes changes partial phase but also alters shared partial amplitude.
• Sabine experimentally verified exponential sound decay in a reverberant room
• Sabine rejected Vitruvius’s vessel sound-enhancement scheme as impossible
• Sabine’s five questions framed the whole research program of architectural acoustics
• Sabine’s formula persists despite relying on an unattainable diffusion ideal
• Ṣafī al-Dīn described sound self-amplification via constructive interference
• Saturn’s ring gaps arise from orbital resonances with its moons
• Saturn’s rings are sculpted by gravitational resonance
• Saturn’s rings flatten because collisions dissipate energy while angular momentum stays fixed
• Sauveur discovered that multiple vibration modes coexist simultaneously on one string
• Savart’s cup demonstrates quarter-wave tube resonance via a bow-driven metal cup
• Saxophone’s cone shape makes it overblow an octave
• Scaling geometry by eta requires dividing frequency by eta in air
• Schlieren photography made invisible shock waves in air directly observable.
• Scientists lose objectivity when the subject of study is their own perception
• Scintillation is a ubiquitous refraction phenomenon across light and radio waves
• Scintillation requires a localized source, uneven speed zones, and long travel
• Seasonal autocorrelation shows same-season months correlate positively with imperfect strength
• Seebeck wrongly believed higher partials could reinforce the perceived fundamental partial.
• Self-driven oscillators with wave-feedback forcing resist analytic prediction
• Self-experimentation reveals that individual sound perception varies from the norm
• Semitones are logarithmically equal steps, not linear ones
• Sensation grows with the logarithm of stimulus strength rather than the strength itself
• Shared room acoustics let 1920 phonograph demos fool live audiences
• Sharp spectral peaks, not narrow gaps, drive strong pitch perception
• Sharp-edged phenomena require high-frequency waves far above human hearing
• Shear instability makes vortex timing exquisitely sensitive to perturbation
• Shepard tones are not perceptually identical across the octave.
• Shepard tones create endlessly rising pitch through shifting autocorrelation peaks
• Shepard tones use only power-of-two partials plus amplitude shaping to create the illusion.
• Short sound duration can raise perceived pitch by an octave.
• Shorter time windows necessarily blur frequency knowledge in any signal
• Signals with autocorrelations that decay to zero need continuous spectra
• Simple hybrid instruments require many subtle acoustical principles to explain properly.
• Simple whole-number ratios that rule musical intervals were extended into a cosmic harmony doctrine
• Sinusoids are the indivisible atoms of all sound and vibration.
• Siren hole geometry directly determines pitch and tuned intervals.
• Sitting in a corner amplifies your voice through reflected wall images
• Sitting near walls creates frequency notches from delayed reflections
• Skilled listeners can echolocate even silent objects by their sound absorption.
• Slight mistuning among voices fuses into a single pleasant tone
• Slightly inharmonic piano partials create the instrument’s characteristic timbre
• Slightly mistuned voices perceptually fuse into one pitched tone
• Slow forcing gives stiffness-dominated impedance; sudden forcing gives mass-dominated impedance
• Small speakers exploit the residue pitch effect to create low-pitch sensations
• Small vibrating objects radiate weak sound because source size is far under one wavelength
• Small-integer frequency ratios yield short periodic traces while irrational ratios never repeat
• Small-integer ratio resonances govern Saturn’s ring gaps, affirming a Pythagorean legacy.
• Small-integer ratios cannot govern all musical intervals consistently
• Smaller soundboards stay more resonant because Schroeder frequency scales inversely with size
• Sonic booms arise from the same mechanism as boat wakes
• Sonogram window width is a calculated tradeoff between time and frequency resolution.
• Sonograms visually expose vowel formants as enhanced frequency bands
• Sophie Germain’s mathematical career advanced solely through self-education and correspondence.
• Sound can be amplified without any external power source
• Sound can be captured as permanent physical markings that encode its pitch
• Sound decay time alone cannot distinguish small from large rooms
• Sound from one explosion skipped over near regions and reached far ones
• Sound has historically resisted representation in print while images have not
• Sound hitting a boundary splits into reflected and transmitted parts with no loss
• Sound in air travels at one speed for all wavelengths, unlike water waves
• Sound information propagates slower than average molecular speed
• Sound instruments must balance confinement against letting sound escape
• Sound intensity can be modeled by tracking energy flux through expanding spheres
• Sound is inherently analog, continuous in both time and value
• Sound is the most accessible window onto universal vibration
• Sound loses energy near walls because compression heat escapes and is not returned
• Sound measurement must be frequency-weighted because ears are not uniformly sensitive
• Sound near walls or large vessels is enhanced by scattering regardless of resonator tuning
• Sound phase is inaudible, but bowing depends on phase-shaped physics.
• Sound pressure amplitude falls off as the inverse of distance from a source
• Sound pressure level depends on oscillation amplitude, not average pressure
• Sound propagates because unbalanced forces accelerate neighboring air cells in sequence
• Sound propagation is symmetric between source and receiver when the medium is stationary.
• Sound refracts toward slower-speed regions over long outdoor distances
• Sound scattering, not tuning, explains voice enhancement from vessels
• Sound speed in air follows molecular kinetic theory prediction
• Sound speed was first measured using a human speaking rate as the clock
• Sound traveling 100 miles takes about eight minutes to arrive.
• Sound-producing objects can be virtually simulated by computing surface motion acceleration
• Sound-radiation efficiency depends on piston size relative to wavelength, not absolute size
• Soundboard resonances shift lower-register piano string tunings via impedance loading
• Soundboards are designed to minimize short-circuiting by lowering critical frequency
• Soundboards deliberately avoid isolated high-Q resonances
• Sounding boards do not amplify every frequency via resonance
• Soundpost and bassbar create asymmetric plate modes to boost radiation
• Sounds within one critical band cause neural interference producing dissonance
• Speaker arrays can synthesize convincing reverberation where none exists naturally.
• Speaker spacing below half a wavelength to avoid aliasing is practically prohibitive
• Speaking trumpets served as naval voice amplification for centuries.
• Specific flat aluminum shapes ring as pure sustained tones when handheld
• Spectral peak sharpness is bounded by the duration of echoes
• Spectral refinement continues until echoes escape or dissipate
• Specular reflection obeys equal incidence and reflection angles locally on curved surfaces
• Speech horns need meter-wide bells to avoid coloring male voices
• Speech rate can be adjusted independently of pitch through time shifting
• Speed of sound depends on temperature, not pressure
• Spreading sound waves weaken because their fixed energy dilutes over an expanding sphere
• Stacking perfect fifths yields the octave, fifth, and fourth intervals.
• Stacking three tubes tuned to octave and twelfth enrich an instrument’s timbre
• Stair reflections diffract off stair edges, producing a descending chirped echo
• Standing waves are equal-amplitude counterpropagating traveling waves
• Steady driven motion oscillates at the drive frequency, never the natural one
• Steady state emission depends on power supply, not internal stored energy
• Stick-slip friction from rosin drives the violin’s sustained oscillation
• Stick-slip friction generates sound vibration in chalk, violins, and scribes
• Strength G measures how room scale dilutes sound energy independent of T60
• Stretched partials give the piano its characteristic musical color
• Stretching partials while keeping fundamentals fixed sounds horrible due to partial collisions
• Striking at a partial’s node suppresses that partial from the sound
• Striking near a string’s fixed end cancels the sound
• String mode shapes are sinusoidal even for finite bead counts
• String pitch rises with tension and falls with length and density
• String vibration is driven by changing force direction, not changing tension
• String-length ratios of small integers produce the most consonant musical intervals.
• Strings alone are nearly inaudible; their sounding boards radiate the sound.
• Stroh violins were invented to direct string sound into early recording horns
• Strong resonances cannot be packed tightly because they drain surrounding power
• Sub-threshold echoes color sound and can even impart pitch
• Sudden surface motion is required to produce an audible pop or boom.
• Suddenness of displacement, not speed, determines whether a boom is audible
• Superposed sinusoids with incommensurate frequencies yield nonperiodic motion
• Superposed sounds cancel or amplify locally without changing each other
• Superposed vibrations produce a net displacement that is the sum of the individual sinusoids
• Superposed vibrations with unrelated frequencies never repeat their overall shape
• Superposition lets separate experiments be combined to predict simultaneous ones
• Superposition of imploding double-layer plane waves explains why cone reflection flips pulse phase
• Superposition of normal modes with chosen amplitudes reproduces any shape
• Supersonic bending waves radiate sound in strongly favored directions
• Surface acceleration, not velocity or motion itself, produces the sounds we hear.
• Surface porosity, not mass, determines how much sound walls absorb
• Sympathetic plate vibration requires correct phase and location matching
• Sympathetic resonance theory of hearing dates to Aristotle about 350 BCE
• Synchronized rhythmic motion from ordinary dancers can resonate a huge building
• Systematically stretching all partials in a chord can reduce its dissonance
• Tapping a bell at different points reveals distinct compass-note partials
• Teakettle whistles are Helmholtz resonators whose resonance sets the pitch
• Temperament matters little when notes are too brief to establish precise frequencies.
• Temperature autocorrelation reveals weather’s daily and seasonal periodicities.
• Temperature inversion layers refract sound away and create silent zones
• Temporal envelope alone, not spectral content, determines much of perceived timbre.
• Textbook oscillator models misrepresent real-world resonance phenomena
• The 1819 siren makes sound via rapid air puffs from a rotating disk
• The accepted textbook claim of bell treble boost fails once loudness differences are normalized
• The air column alone vibrates; wall material only sets its shape
• The auditory cortex can fabricate sounds indistinguishable from real perception
• The auditory system performs pitch analysis as autocorrelation per sub-band, summed into a correlogram.
• The basilar membrane’s fixed-spread frequency resolution shrinks relative bandwidth as frequency rises
• The biodegradable Sun Chips bag was 100 times louder than a normal chip bag
• The brain suppresses equally loud sound in one ear to convey source direction instantly
• The bridge sits away from edges because clamped-edge phase inversion cancels proximity advantage
• The bridge transduces string vibration via tuned rocking and squatting resonances
• The bridge’s single early echo creates a broad 2300 Hz response peak.
• The bullwhip crack is a supersonic shock wave created by impedance matching
• The central debate in pitch perception is whether humans are essentially walking Fourier analyzers
• The circle of fifths leap of 210.587 degrees is a 149.413-degree clockwise step
• The cochlea’s two outer chambers are one continuous tube connected at the apex
• The conical horn converts a closed-reed tube into a full harmonic instrument
• The ear does more than Fourier-analysis of partials
• The ear does not automatically decompose sounds into their sinusoidal components
• The ear does not mechanically ring on like a string after sound stops
• The ear does not receive copies of the source’s physical motion.
• The ear perceives a virtual pitch not physically present in a sound’s components
• The ear substitutes a real partial for a just-damped piano tone
• The ear unconsciously substitutes same-pitch partials to continue a decaying note
• The ear’s nonlinear mechanics can physically generate missing combination frequencies
• The Edison gramophone amplifies sound via a loading chamber
• The first human voice recording predates Edison by seventeen years
• The fixed energy of an impulse forces increasing echoes to weaken proportionally.
• The flute is the oldest manufactured instrument, dated 30-40,000 years
• The flute is the oldest manufactured instrument, from hollow bones 40,000 years ago
• The flute’s cork, not just its tube, shapes the instrument’s timbre
• The frequency-wavelength-speed relation governs waves in every medium.
• The fundamental theorem of arithmetic prevents reaching the octave by perfect fifths
• The gas filling a resonant cavity shifts its Helmholtz frequency.
• The human oral cavity functions as an adjustable Helmholtz resonator
• The inharmonicity of real strings is a desirable feature, not a defect
• The last echo time sets the minimum width of spectral peaks.
• The Mach cone shock wave is the three-dimensional analog of a boat’s V-shaped wake
• The major and minor sixth ratios derive by complementing thirds within an octave
• The middle ear’s three tiny bones act as a mechanical impedance transformer
• The modal decomposition of vibration resisted even brilliant thinkers historically.
• The nervous system can synthesize tones from temporal periodicity alone
• The ocarina predates European contact by 12000 years
• The octave and perfect fifth are mathematically incompatible, forcing the fifth’s compromise.
• The octave-shifted echo likely arose from Bragg-like periodic spacing of plantation trees
• The Ohm-Helmholtz phase law holds only approximately, not fundamentally
• The ossicle-softer-ligament design protects ears by dumping intense-sound energy.
• The period of a sinusoid is the inverse of its frequency
• The period of summed sinusoids equals the lowest common period
• The phon unit anchors loudness to perceived equality across frequencies rather than raw SPL
• The phonautograph’s inventor intended visual transcription, not playback
• The pianoforte’s hammer mechanism enabled dynamic control that plucked strings lacked
• The pinna’s convoluted shape exists to encode sound direction via reflections
• The pinna’s folded shape encodes sound direction as spectral echoes
• The player’s mouth cavity resonates with the instrument and shapes its timbre
• The power spectrum is the Fourier cosine transform of the autocorrelation
• The Reynolds number makes flow behaviors scale-invariant across wildly different sizes
• The Sabine formula assumes diffuse sound that real rectangular rooms rarely produce
• The saxophone was laboratory-engineered, as most instruments were not
• The sensation of a real tone may depend partly on internally generated neural signals
• The seventh and eleventh string harmonics are substantially flat relative to equal temperament
• The simple bell-boosts-treble explanation of trumpet tone is incomplete.
• The singer’s formant arises from a laryngeal cavity resonance shaped by false vocal folds
• The sinusoid-to-pure-tone link is the one stable pillar of pitch perception.
• The siren showed sinusoid partials arise without any sinusoidally vibrating source
• The speaking trumpet was the only voice amplification system for centuries
• The stick-slip bow interaction self-limits and adapts energy to the drain.
• The string drives the sounding board that produces nearly all the sound.
• The Strouhal relation predicts audible howls from ship shrouds but none from islands
• The tabla achieves near-harmonic modes through membrane density variation
• The time-domain impulse view explains acoustic phenomena that frequency analysis only describes
• The time-energy uncertainty principle is really a time-frequency uncertainty principle in disguise
• The tuning fork was invented in 1711 by trumpeter John Shore
• The uncertainty principle relates resonance width to decay time
• The violin body is a Helmholtz resonator responsible for its tone.
• The violin bridge acts as a frequency-tuned impedance-matching intermediary
• The violin bridge acts as the energy gatekeeper between strings and body
• The violin bridge’s carved resonance boosts treble frequencies to shape timbre
• The violin can be analyzed as an energy chain from bow to air
• The violin’s harmonics are phase-locked so their sum produces a traveling kink
• The vocal tract actively amplifies speech rather than merely filtering it
• The voice drives the tract noninteractively whereas trumpet lips receive feedback
• The wolf tone arises from impedance-matched bridge-body resonance feedback
• Thick shrubs barely block noise because they act as a slower continuum
• Thirteenth-century physics intuited sound self-amplification through reflection.
• Thirteenth-century theory described self-amplification of wind instruments
• Three-dimensional rooms yield denser mode distributions at higher frequencies
• Throat chamber echoes raise impedance by in-phase amplitude buildup
• Thunder originates as a supersonic shock wave that quickly decelerates to ordinary sound speed.
• Timbre depends on sound order over time, not just spectral content.
• Timbre is determined by the relative amplitudes of partials, not their frequencies alone
• Time-delayed reflections impose periodic comb filters of enhanced and suppressed frequencies
• Time-delayed repetition of sound produces a matching repetition pitch
• Time-delayed sound self-addition imposes spectral notches via autocorrelation
• Time-frequency uncertainty applies both to the sound source and the analysis window.
• Tiny periodic signals can be recovered from heavy noise via autocorrelation
• Tire noise lacks a settled generation mechanism and control solution
• To reproduce a frequency faithfully you must sample at least twice its rate
• Tongue and jaw position move the first two formant frequencies
• Tongue and lip constrictions shift vocal resonances mostly near their nodes, not antinodes.
• Too much outcoupling kills resonance just as too little silences it
• Torso and pinna echoes encode sound source direction cues
• Total damping equals neck friction plus radiated sound, with friction dominant
• Trained singers project an extra formant near 2800 Hz that cuts through orchestral sound
• Trapped air in a drum bowl alters the head’s mode frequencies from ideal values
• Treating air as communicating cells explains propagation, reflection, and diffraction
• Treating room walls as mirrors locates where early reflections need absorbing.
• Treble boost from trumpet bells may not actually make high frequencies louder
• Tree spacing and viewing angle mathematically reproduce the octave-up echo.
• Trumpet lips act as a damped oscillator resonating near 95 Hz.
• Trumpet lips open on high pressure because notes are played above resonance
• Tube end conditions determine which harmonic partials an instrument produces
• Tube geometry determines which partials resonate and so shapes timbre
• Tuned resonators cancel duct fan noise without blocking airflow
• Tuning tubes to octave and twelfth partials produces a more pleasing tone
• Turbulent jet noise is scale-invariant across 256-fold size differences
• Tuvan overtone singers merge formants to amplify single harmonics into a distinct second melody
• Twinkling is one instance of the universal scintillation phenomenon
• Two coupled modes split above and below the test frequency, causing beat frequencies
• Two frequencies can mechanically generate sum and difference frequencies in the ear
• Two inaudible high tones can produce audible low phantom tones that interfere
• Two opposing coupled resonances can cancel response at intermediate frequencies
• Two simultaneous tones generate audible lower tones absent from the stimulus
• Two- and three-dimensional systems show rapidly rising modal density
• Ultra-thin carbon-nanotube films can act as thermoacoustic loudspeakers
• Ultrathin thermoacoustic films can turn entire walls and clothes into loudspeakers
• Uncertainty principles force mechanical frequency sorting in the ear to be coarse.
• Underground rock strain release can launch surface sod upward via focusing
• Understanding two coupled oscillators generalizes to arbitrarily complex systems
• Undiscovered ring-while-held plate shapes with multiple resting zones remain to be found
• Uneven intervals make Just intonation scales impossible to transpose freely.
• Uneven scale intervals make free transposition impossible
• Unexplained boom phenomena recur independently at scattered sites worldwide.
• Velocity response is the convenient quantity for impulse power
• Velocity, not displacement, is the convenient quantity for impulse analysis
• Vent holes can acoustically cancel specific membrane modes by short-circuiting
• Very early reflections can resonantly boost power across the whole audible range
• Vibrational pseudoscience has defrauded large sums through fake energy machines.
• Vibratory pseudoscience exploited Chladni patterns to defraud millions.
• Violin bridge motion must be modeled together with the top plate, not alone
• Violin high-frequency radiation is directional once wavelength approaches instrument size
• Violin quality differences hide in time-domain impulse responses that Fourier analysis erases
• Violin timbre changes with direction as high frequencies become increasingly directional
• Viscosity measures how strongly fluid layers drag one another
• Vision and sound expectations must concord for convincing audio-scene perception
• Visual sound traces cannot uniquely capture what listeners perceive as the same vowel
• Visual speech-feedback training fails because identical percepts can have different sound traces
• Visualizing sound traces directly inspired the electronic microphone and telephone
• Vitruvius described Helmholtz resonant modes, not mere amplification
• Vitruvius’s bronze theater vessels were Helmholtz resonators
• Vitruvius’s resonator scheme has gone empirically untested for millennia
• Vocal fold oscillation frequency is predictable without invoking aerodynamic forces
• Vocal fold waveform shape with rich harmonics is what makes speech possible
• Vocal folds drive the tract one-way, unlike the interactive trumpet feedback loop
• Vocal resonance cannot bend notes up, only lip pressure can.
• Vocal tract coupling reinforces the reeded air column by lowering its resonant frequency.
• Vocal tract length and larynx size determine sex-typical pitch and formants
• Vocal tract resonances measurably shape wind instrument timbre
• Vocal tract shape determines voice timbre far more than vocal cords do
• Vocal tract wall softness and open-end impedance mismatch lower resonance Q
• Vocalizing during a whistle reveals that the whistle matches the second formant
• Voiceless sounds arise from varied vocal tract constrictions independent of vocal folds
• Vortex rings are toroidal flows that self-propel away from their source
• Vortex shedding alternates as each new vortex forms and forces its predecessor downstream
• Vortex shedding becomes audible sound despite wasting most energy as heat
• Vortex shedding causes violent oscillation through cooperative lockin resonance
• Vortex shedding frequency depends on flow speed and wire size, not wire tension
• Vortex shedding from aircraft surfaces is both loud and a drag source
• Vortex shedding spans scales from sub-audible pitches to hour-long ocean eddies
• Vortices form spontaneously only when ambient turbulence and vibration are removed
• Vowel identity is carried by upper partial tones, not fundamentals
• Vowels are distinguished by formant frequencies controlled by tongue, jaw, and lips
• Wall friction and resonance oppose each other in determining instrument sound radiation.
• Wall friction converts organized oscillating air motion into heat, damping sound
• Wall losses, not radiation, dominate resonance damping in narrow pipes
• Wall proximity alternately boosts or suppresses a source depending on phase.
• Wallace Clement Sabine founded the science of architectural acoustics in 1895
• Wallace Sabine’s acoustics research began with a request from Harvard’s president
• Wallace Sabine’s acoustics work began at Harvard’s request in the 1890s
• Walls absorb sound by converting organized acoustic energy into heat through friction
• Walls and corners near a sound source increase its power output
• Water damping is thousands of times stronger than air damping
• Water reflects about 99.9 percent of airborne sound at its surface
• Wave period stays constant across media while wavelength and speed change
• Wave phenomena can be studied with scaled-down mockups by scaling frequency inversely to size.
• Wave speed on a string depends only on tension and density, not frequency
• Wave speed, frequency, and wavelength are linked by fλ = c
• Wave speed, wavelength, period, and frequency are locked by c equals f times lambda
• Waveform beat rate depends on the lower partial’s frequency, not just the mistuning amount
• Waveforms become non-periodic because higher normal-mode frequencies are not equally spaced
• Waves always refract toward regions of slower wave speed
• When a string’s linear density is fixed, pitch is varied by tension and length
• Whether a sound parses into separate notes is decided by perception, not physics
• Whether a surface reflects or scatters waves depends on roughness relative to wavelength
• Whether a surface reflects specularly or diffusely depends on wavelength, not polish
• Whether echoes constructively add in Fourier analysis depends on wavelength relative to echo timing.
• Whether two vibration frequencies are commensurate with small integer ratios shapes their musical meaning
• Whispering provides white noise that reveals vocal tract formants
• Whispering replaces vibrating vocal folds with jet turbulence as the sound source
• Whistle pitch derives from vocal tract resonances, not the oral cavity’s Helmholtz resonance
• Whistling arises from vortex formation in a sheared jet boundary layer
• Whistling sound arises from cooperative resonance between lip vortices and vocal tract formants
• White noise has autocorrelation only at zero time shift.
• Widening a sound’s bandwidth makes it seem louder at equal total power
• Widening partial near-coincidences by stretching lowers dissonance
• Widespread sonic booms need not originate from supersonic sources
• Wind chime tongues are tuned so their mechanical bending matches the tube’s air resonance.
• Wind gradients refract sound toward slow regions and extend its range
• Wind instrument design still depends on art and intuition rather than computation
• Wind instrument resonances resist aligning into a harmonic series because of impedance-mismatch reflections.
• Wind instruments resonantly amplify only frequencies that reflect back at the drive period
• Wind speed gradients, not wind itself, refract sound and break reciprocity
• Wind-borne pitch rises with velocity and with smaller obstruction size
• Wind-instrument harmonic phases are set by resonant pulse enhancement, not chance.
• With sufficient dissipation, closed and open resonant systems become spectrally equivalent
• Without friction, resonances can both expel particles and later restore them indefinitely.
• Wolf tones require body modes that strongly rock the bridge, not just any resonance
• Wood grain alignment steers bending waves because trees resist wind
• Wood grain direction changes bending wave speed and radiative efficiency
• Wood’s anisotropy makes sound radiation direction- and frequency-dependent
• Writing is an early digital technology that never degrades with copying