Time-delayed reflections impose periodic comb filters of enhanced and suppressed frequencies

Evidence

A τ ms time delay enhances frequencies around n/τ, n = 1,2,.. . Hz and suppresses frequencies around (n – 1/2)/τ, n = 1, 2,.. . Hz. Thus a 5 ms time delay (corresponding to a 1.7 m path length difference) enhances a comb of frequencies around 200, 400, 600, … Hz and suppresses a comb of frequencies around 100, 300, 500,… Hz. A 25 ms delay, corresponding to a more common concert hall path difference of 8.5 m, still too short to be heard as an echo, enhances a comb of frequencies around 40, 80, 120,… Hz and suppresses a comb of frequencies around 20, 60, 100,… Hz. — Eric J. Heller, Why You Hear What You Hear- An…, 2550

Categorization

• DEFINE: Quantifies exactly how reflection delay maps to spectral comb spacing — the n/τ enhancement formula is load-bearing.
• SEED: A possible essay angle: how the ‘comb filter’ mathematics of echo explains why the same room sounds dramatically different for different notes and instruments.