Hong Life CalculatorsUnderstanding the comb filter and speaker delay calculator — concept and principle
When the same sound reaches a listener or microphone by two paths of different length, the two copies arrive slightly out of step. At some frequencies they add, at others they cancel, and the frequency response takes on a series of evenly spaced dips that looks like the teeth of a comb. This calculator turns a path difference into the time delay, the first cancellation frequency and the spacing between cancellations.
How it is calculated
- Delay: τ = d / c, shown in milliseconds (× 1,000).
- First notch: f₁ = c / (2d) = 1 / (2τ).
- Notch spacing: Δf = c / d = 1 / τ.
Here d is the path difference in metres and c the speed of sound in m/s (about 343 m/s in air at 20 °C). Notches occur at f = (2k + 1) / (2τ) for k = 0, 1, 2, …
The principle
Delaying a sine wave by τ shifts its phase by 360° × f × τ. Cancellation happens when the delayed copy is exactly half a cycle (180°) behind, which first occurs when τ equals half a period, f = 1/(2τ). Every additional full cycle of delay produces another cancellation, so notches repeat every 1/τ hertz. Halfway between notches the copies are in phase and add, giving peaks up to 6 dB above a single copy. On a logarithmic frequency axis the notches crowd together toward high frequencies, producing the hollow, phasey sound typical of comb filtering.
Worked example
- Inputs: d = 1 m, c = 343 m/s.
- Delay: 1 / 343 = 0.0029155 s = 2.915451895 ms.
- First notch: 343 / (2 × 1) = 171.5 Hz.
- Notch spacing: 343 / 1 = 343 Hz, so further notches fall at 514.5 Hz, 857.5 Hz and so on.
| Speed of sound (m/s) | Delay (ms) |
|---|---|
| 85.8 | 11.66180758 |
| 172 | 5.83090379 |
| 257 | 3.887269193 |
| 343 | 2.915451895 |
| 429 | 2.332361516 |
| 514 | 1.943634597 |
| 686 | 1.457725948 |
How to read the result
Small path differences push the first notch up: 10 cm gives about 1.7 kHz, which affects voice clarity. Large path differences put notches very close together, and above a few metres the ear tends to hear a separate echo rather than a tonal colouring. To align a delay speaker with a main speaker, delay the closer one electronically by the computed τ so both wavefronts arrive together at the listening position. The depth of each notch depends on how equal the two levels are; equal levels give deep notches, while a copy 6 dB quieter gives much shallower ones.
Common mistakes
- Using the total path length instead of the difference between the two paths.
- Forgetting that the speed of sound changes with temperature (about 0.6 m/s per °C).
- Expecting one delay setting to fix every seat; the path difference varies with position.
Frequently asked questions
Why does my microphone sound hollow near a table?
Sound reflected from the table travels a slightly longer path and creates a comb filter with the direct sound. Moving the microphone or using a boundary microphone helps.
Can two microphones on one source cause this?
Yes. If they are at different distances and mixed together, the difference in path creates comb filtering; the 3:1 distance guideline helps reduce it.
Sources: F. A. Everest and K. C. Pohlmann, Master Handbook of Acoustics, McGraw-Hill · T. D. Rossing, F. R. Moore and P. A. Wheeler, The Science of Sound, Addison-Wesley