A returning echo creates power-spectrum peaks spaced by its inverse time

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

Categorization

• DEFINE: Defines the proximity resonance at zero frequency and how echo timing sets spectral peak spacing.
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 1096
• XREF: connects to: Loudness-time functions reveal echoes and reverberation better than level-time ones; Echo interference creates sinusoidal power fluctuations that average to zero; Repetition pitch equals the reciprocal of the echo delay time (+8 more)

Broader Connections

• Repetition pitch equals the reciprocal of the echo delay time #corroborates (0.85)
• Room echoes sculpt sharp resonant peaks into a sound’s spectrum #exemplifies (0.85)
• Any echo-producing system inevitably exhibits frequency power fluctuations #expands (0.80) — Eric J. Heller, Why You Hear What You Hear- An…, 1163
• Whether echoes constructively add in Fourier analysis depends on wavelength relative to echo timing. #qualifies (0.80)
• Echo interference creates sinusoidal power fluctuations that average to zero #complicates (0.75)
• Echoes rearrange spectral energy without changing its total #expands (0.75)
• Long sound durations are required for narrow frequency spectra #complicates (0.75)