The last echo time sets the minimum width of spectral peaks.

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 (#expands, via linked claim)

Categorization

• XREF: connects to: A returning echo creates power-spectrum peaks spaced by its inverse time — Eric J. Heller, Why You Hear What You Hear- An…, 1096; Long sound durations are required for narrow frequency spectra; Faster sound decay broadens spectral peaks in observed spectra (+2 more)

Related

• A returning echo creates power-spectrum peaks spaced by its inverse time (similarity 0.90)
• Loudness-time functions reveal echoes and reverberation better than level-time ones (similarity 0.84)
• Spectral peak sharpness is bounded by the duration of echoes (similarity 0.81)
• Later echoes refine the spectrum into sharper peaks limited by the echo delay (similarity 0.79)

Broader Connections

• A returning echo creates power-spectrum peaks spaced by its inverse time #expands (0.90) — Eric J. Heller, Why You Hear What You Hear- An…, 1096
• Faster sound decay broadens spectral peaks in observed spectra #corroborates (0.85)
• Repetition pitch equals the reciprocal of the echo delay time #corroborates (0.80)
• Long sound durations are required for narrow frequency spectra #qualifies (0.75)
• Gaussian gating minimizes the bandwidth-duration product for tone bursts. #corroborates (0.70)