Frequency measured in Hertz is dimensionally inverse seconds

Evidence

Echoes cause the power spectrum to develop structure. The features resulting from returning echoes are evident in figure 11.2. The first return echo at time T = 1/f induces broad peaks in the power spectrum, spaced by a frequency interval f. The reason for the broad peaks can be seen from the cosine transform, shown for one particular frequency in the middle column in figure 11.2. In the case of the free edge, for example, the product of the cosine of frequency f and the echo is positive at the return time T and adds to the positive contribution at time zero. Thus the second peak lies at frequency f. The first peak is at zero frequency—the proximity resonance. — Eric J. Heller, Why You Hear What You Hear- An…, 1096 (#exemplifies, via linked claim)

Fourier further theorized that if he combined enough sine waves together he could exactly model any waveform in existence. This allowed him to develop the Fourier transform pair—two equations that provide a means of transforming the time domain into the frequency domain and back. — David Howard, Jamie Angus, coustics and Psychoacoustics, 440 (#expands, via linked claim)

The temporal theory of pitch perception is based on the fact that the waveform of a sound with a strong musical pitch repeats or is periodic (see Table 3.2). An example is shown in Figure 3.1 for A4 played on four instruments. The f0 for a periodic sound can be found from a measurement of the period of a cycle of the waveform using Equation 3.1. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 891 (#expands, via linked claim)

Categorization

• XREF: connects to: The period of a sinusoid is the inverse of its frequency; The fundamental frequency of a pitched sound is measurable from its waveform period — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 891; A returning echo creates power-spectrum peaks spaced by its inverse time — Eric J. Heller, Why You Hear What You Hear- An…, 1096 (+4 more)

Related

• A returning echo creates power-spectrum peaks spaced by its inverse time (similarity 0.84)
• The fundamental frequency of a pitched sound is measurable from its waveform period (similarity 0.83)
• The Fourier transform pair converts signals between time and frequency domains (similarity 0.83)
• Real signals contain smooth distributions of infinite frequencies (similarity 0.81)
• Echoed sounds spaced 1-10 ms generate a perceived pitch of 100-1000 Hz (similarity 0.81)
• Certain processes are far easier to analyze in the frequency domain than in time (similarity 0.81)
• Whether echoes constructively add in Fourier analysis depends on wavelength relative to echo timing. (similarity 0.81)
• Loudness-time functions reveal echoes and reverberation better than level-time ones (similarity 0.81)
• Listening analyzes periodic sound into integer-multiple sine components (similarity 0.80)
• Fourier analysis of echoes yields alternating strong and weak spectral bands (similarity 0.80)
• Every wave-like quantity has an uncertainty principle tying its Fourier transform pair (similarity 0.80)
• Pitch, though subjective, is measurable in Hz by matching against a sine wave (similarity 0.80)
• Pitch of periodic sounds is determinable from the waveform’s cycle period (similarity 0.80)
• Listeners reconstruct a perceived pitch that is not physically present (similarity 0.80)
• Complex real-world sounds can be analyzed via Fourier analysis (similarity 0.80)

Broader Connections

• A returning echo creates power-spectrum peaks spaced by its inverse time #exemplifies (0.85) — Eric J. Heller, Why You Hear What You Hear- An…, 1096
• The fundamental frequency of a pitched sound is measurable from its waveform period #expands (0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 891
• The Fourier transform pair converts signals between time and frequency domains #expands (0.80) — David Howard, Jamie Angus, coustics and Psychoacoustics, 440
• Pitch, though subjective, is measurable in Hz by matching against a sine wave #corroborates (0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 827
• Long sound durations are required for narrow frequency spectra #expands (0.75)