The period of a sinusoid is the inverse of its frequency
Evidence
Since it is going around at constant speed, the motion of the ball starts to repeat itself after exactly one revolution. The time it takes to go one revolution is called the period T, and the motion we say is periodic with period T. T is a solution to the equation 2π fT = 2π, i.e., T = 1/f. The period is simply the inverse of the frequency. — Eric J. Heller, Why You Hear What You Hear- An…, 255
Categorization
Category: Definitional Content
- DEFINE: Establishes the period-frequency relation T = 1/f, a foundational relation for all of acoustics.
Related
- Only a sinusoid has a single frequency; every other shape contains multiple frequencies (similarity 0.83)
- Sine waves are the simplest periodic excitation, and all complex waveforms decompose into them (similarity 0.80)
- Only a pure sinusoid comprises exactly one frequency. (similarity 0.80)
- Superposed sinusoids with incommensurate frequencies yield nonperiodic motion (similarity 0.79)
Broader Connections
- Frequency measured in Hertz is dimensionally inverse seconds
#qualifies(0.80) — Eric J. Heller, Why You Hear What You Hear- An…, 257 - Only a sinusoid has a single frequency; every other shape contains multiple frequencies
#expands(0.75) — Eric J. Heller, Why You Hear What You Hear- An…, 332 - Any complex waveform can be decomposed into simple sine waves
#expands(0.72) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 135 - Superposition lets complex waveforms be solved as sums of sine wave solutions
#exemplifies(0.70) — David Howard, Jamie Angus, coustics and Psychoacoustics, 439