Mixing a signal with a slightly delayed copy of itself produces comb filtering

When a signal is mixed with a delayed copy of itself, each frequency lands in a different phase relationship: components reinforce where the delay equals a whole number of wavelengths and cancel where it equals an odd number of half-wavelengths. Across the spectrum this yields a series of regularly spaced peaks and deep notches resembling the teeth of a comb. The notch spacing is inversely proportional to the delay: the first null is at f = 1/(2·delay), with further nulls every 1/delay — so shorter delays push the comb higher. A 0.5 ms delay cancels 1 kHz (and 3, 5 kHz…) while reinforcing 2, 4 kHz; delays beyond ~25 ms are heard as distinct echoes rather than timbral change. This is heard as a hollow, phasey coloration and worsens frequency-response evenness and feedback behavior. It differs from polarity inversion: flipping a waveform also cancels, but by inversion, not delay — the loose term ‘180 degrees out of phase’ conflates the two. Comb filtering arises wherever one sound reaches a point by two paths: two speakers at unequal distances, two mics on one source, wall reflections, or a direct signal mixed with a short electronic delay.

Examples

A 1 ms delayed copy mixed with the direct signal puts the first null at 500 Hz, with further nulls at 1.5 kHz, 2.5 kHz, and so on. Two floor monitors playing the same mix from different distances comb-filter at center stage: uneven response and higher feedback risk.

Assessment

A signal is mixed with a copy delayed by 0.5 ms: name two frequencies that cancel and two that reinforce, and explain how comb filtering differs from polarity inversion despite both cancelling. Two speakers play the same signal and a listener is ~1 foot (~0.9 ms) farther from one — estimate the first cancellation notch, and explain why moving the listener shifts the notch frequencies.