Tertiary Source

Musical Doppler self-sonar

2008-11-14 18:42:18

If you stand reasonably close to a road, the sounds of passing traffic get Doppler shifted: they start off high and end up low, "wheeeee-oooooom." Professional and amateur musicians have sophisticated training in recognizing frequency ratios. (Though, explicitly mentioning the relationship between frequency/wavelength ratios and intervals is more common when players of string instruments experiment with making harmonics.) How accurately could you estimate the speed of a passing vehicle by the sound it makes?

If the doppler-shifted frequency is
f =
f0
1 + v/c
,
where v is the speed of the traffic and c = 767 mph is the speed of sound, then the ratio of the frequencies before and after is
fhigh
flow
=
1 + v/c
1 - v/c
.
Turns out that some familiar intervals correspond to some common speed limits:
Interval fhigh/flow v/c v
minor second 16/15 1/31 25 mph
major second 9/8 1/17 45 mph
minor third 6/5 1/11 70 mph
major third 5/4 1/9 85 mph
perfect fourth 4/3 1/7 110 mph
perfect fifth 3/2 1/5 150 mph
octave 2/1 1/3 250 mph
That suggests that someone with enough of an ear to know "that's a major third" or "that's between a half step and a whole step" would be able to tell the speed of a passing vehicle to within ten or fifteen miles an hour. This would be a fun parlor trick.
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