Walk the Quiet Lines
Two speakers playing the same note fill a room with fixed lines of silence. Pace out the gaps between them and you have measured the speed of sound without timing anything.
What it is
Two speakers at the top, one tone, and you somewhere in the room. Drag yourself about.
The bright fans are where the two arrivals add up and the black wedges are where they cancel. They’re not moving. Walk into one and the sound goes away while both speakers carry on playing at you.
The line across the room is where the measurement is taken, and the dots on it are the quiet lines crossing it.
How it works
Sound from two sources reaches you having travelled two different distances. Where that difference is a whole number of wavelengths they add, where it’s a whole number and a half they cancel, and since the sources are not moving neither are the lines.
Cancellation needs sin θ = (n + ½) λ / D, and that has a limit worth noticing: if half a
wavelength is longer than the gap between the speakers there is nowhere at all that cancels.
At 200 Hz with the speakers half a metre apart, the room has no quiet lines in it.
The measurement is the other way round. Count the quiet lines, measure their spacing, and since you know what frequency you were playing, out comes the speed of sound. No clock, no stopwatch, nothing timed.
| tone | wavelength | lines each side | sweep used | by even spacing | from the angles |
|---|---|---|---|---|---|
| 450 Hz | 76.2 cm | 2 | ±6 m | 363 m/s | 344 m/s |
| 900 Hz | 38.1 cm | 3 | ±6 m | 391 m/s | 344 m/s |
| 1800 Hz | 19.1 cm | 6 | ±6 m | 413 m/s | 344 m/s |
| 900 Hz | 38.1 cm | 3 | ±1.6 m | 348 m/s | 344 m/s |
The true figure is 343.
What surprised me
The ruler is only a ruler near the middle, and I nearly published the wrong number. The first version of the measurement did the obvious thing: average the gap between neighbouring quiet lines, multiply by the speaker separation, divide by the distance. That’s the standard two-slit formula and it gave 391 m/s, which is fourteen per cent out, and it looked completely plausible sitting under a picture of an interference pattern.
The fault is one substitution. Cancellation depends on sin θ, and the spacing formula quietly
replaces that with x / L, which is the same thing only for small angles. The outer quiet
lines in that sweep sit at thirty seven degrees, where the two differ by a fifth.
Look at what it does across the table. Wider sweep, worse. Higher frequency, worse, because a shorter wavelength puts more lines further out. 363, then 391, then 413, all from the same room with the same speed of sound in it. Restrict the sweep to the middle 1.6 metres and it comes back to 348.
Fitting the angles instead gives 344 every time, on every sweep and every frequency, and the page now reports both so the gap between them is visible rather than hidden.
Painting the field needed the falloff taken out of it. Sound spreads as 1/r, so a single brightness scale for the whole room blows out the near field to solid white and leaves the far field black, and the pattern is invisible in both. Normalising each row against the centre line at the same depth shows the interference and nothing else.
That’s a display choice rather than a measurement, and it’s worth saying which is which: the picture has the spreading divided out, the numbers do not.
What I would do next
Put a wall in. Everything here is two sources in open space, and a real room adds its own copies of them in every surface, so the pattern isn’t six fans, it’s six fans plus the fans from every image source the walls create. That’s why a room has a bass problem in one corner and not another.
The image source method is the same arithmetic pointed at a mirror, and it would turn this from a demonstration into something you could actually stand in.
The other thing missing is that the quiet lines are only truly quiet for one frequency. Play two tones and the nulls of one sit on the peaks of the other, which is most of why real music doesn’t disappear when you move your head, and it would make the difference between a physics picture and a listening one.