One Fifth as Fast

This weekend Danielle and I rode our bikes along the “Grand Rounds” — a string of parks in Minneapolis that are connected by biking trails. We covered 25 miles in two and a half hours. We took the bike path along the new light-rail track back from Minnehaha Creek Trail up to Washington Ave near the MetroDome. The train passed by a few times, and at one point I noticed the Doppler Effect as I biked past a ringing warning light.
You normally think of the doppler effect as a change in the pitch of a sound when the source of the sound passes you. For example the vrooom sound of the Indy 500, or an ambulance siren. But it also happens when you are the one moving and the source of the sound is stationary.
When the distance between the sound source and the listener is getting smaller, the pitch will sound higher to the listener. When the two are moving apart the pitch will sound lower.
You can train yourself to recognize musical intervals. For example, if you hum the first two pitches of “Somewhere Over the Rainbow”, you have an interval called an “octave”. The first interval of Beethoven’s 5th symphony is a “Major Third”. The first interval of the James Bond Theme “For Your Eyes Only” is a “Major Fifth”. The major third, major fifth and octave correspond to frequency multipliers of approximately 1.25, 1.5 and 2.
If you passed right by a continuous tone on your bicycle, and recognized that the pitch changed by, for example, a Major Third, could you deduce how fast you were traveling?
Suppose the tone was a A 440. That means 440 waves would hit your ear each second. As you approach the tone, you would hear a B 494 and after you passed it you would hear G 392. To alter a pitch from 440 to 494 means that you would travel the distance that 54 A 440 waves occupy in one second (the 54 that you hit while you travel plus the 440 that moved towards you would add up to the 494 that you observed). 54 A 440 waves occupy a distance of (340.29 meters per second divided by 440 per second * 54 = ) 41 meters. 41 meters per second is 91 miles per hour.

INTERVAL	# HALF STEPS	SPEED
Diminished Second	1	23 miles per hour
Second	2	45 miles per hour
Minor Third	3	68 miles per hour
Major Third	4	91 miles per hour
Fourth	5	113 miles per hour
Diminished Fifth	6	136 miles per hour
Fifth	7	158 miles per hour
Octave	12	272 miles per hour

Next time you’re watching the Indy 500, see if the doppler effect sound of the racecar engines approaches one octave. Those cars can go as fast as 272 miles an hour at times.
I was waiting to write about this until I could get Becka to help me record some data. I plan to blow a steady pitch on my chickadee okarina while biking down the alley with my laptop recording stuff set up in the driveway. For some reason, Becka hasn’t been too excited to help me with this….