Index Room & AcousticsTime Alignment

Time Alignment

Convert unequal speaker distances into delay, samples and level trim.

Delay speaker A by2.04ms

In samples97.9

Path difference700mm

Trim speaker A by−2.22dB

First cancellation245Hz

Wavefronts leaving both speakers

Speaker A
Speaker B
Listener

Speaker A is closer, so its sound arrives first and pulls the image towards it.

Input

Speaker A to the seatm

Speaker B to the seatm

Apply the delay in the sketch

DSP sample rate (kHz)

Air temperature°C

How it works

Distance is time

Sound covers about 34 cm every millisecond. If one speaker is closer than the other, its sound arrives first, and our hearing places the image at whichever arrives first. Delaying the nearer speaker restores the balance:

\Delta t = \frac{\left|d_A - d_B\right|}{c}

n = \Delta t \times f_s

where $n$ is the delay in samples at the processor's sample rate. A difference of only 10 cm is 0.29 ms, enough to shift a centred voice noticeably.

Level trim

The nearer speaker is also louder. By the inverse-square law the correction is

\Delta L = 20\log_{10}\!\frac{d_{far}}{d_{near}}\ \mathrm{dB}

Why it matters for subwoofers

Two sources carrying the same signal cancel when their paths differ by half a wavelength. The lowest frequency at which that happens is

f_{null} = \frac{c}{2\,\left|d_A - d_B\right|}

If that lands near the crossover between subwoofer and main speakers, a hole appears in the response. Use the distances from the seat to each driver as a first setting, then refine by measurement, since crossover filters add delay of their own.

References

H. Haas, “Über den Einfluss eines Einfachechos auf die Hörsamkeit von Sprache,” Acustica, vol. 1, pp. 49–58, 1951 (Göttingen dissertation, 1949). English translation: “The Influence of a Single Echo on the Audibility of Speech,” J. Audio Eng. Soc., vol. 20, no. 2, pp. 146–159, 1972. AES