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I've noticed the Doppler effect in the change of pitch of music as I ride past on my bicycle, so I assume in the old days people did this on horses too. Are there any ancient mentions or theories about this, maybe the ancient greeks?

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    $\begingroup$ They did not. The Doppler effect for sound was noticed only 3 years after Doppler described it for light in 1842. Wave propagation was not studied much before 19th century, and observations were much more basic. $\endgroup$ – Conifold Nov 17 '17 at 2:42
  • $\begingroup$ @Conifold Acoustics (studied in "music", in the quadrivium sense) has a millennia-long history, though. $\endgroup$ – Geremia Nov 17 '17 at 3:04
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    $\begingroup$ @Geremia Yes, but neither Pythagoreans, nor Aristotle, nor even Leonardo and Galileo listened to music while riding horses, as far as I know. Even the connection between frequency and pitch was only noticed in 17th century. $\endgroup$ – Conifold Nov 17 '17 at 3:08
  • $\begingroup$ @Conifold Alexandre Eremenko's answer below does help explain how it would be hard to notice. $\endgroup$ – Geremia Nov 17 '17 at 17:17
  • $\begingroup$ If you know what you're expecting, it's extremely trivial to observe the Doppler effect for sound using even the most primitive equipment. But many people probably weren't expecting it, or if they did notice it, they didn't think of it as something scientifically interesting. $\endgroup$ – Ben Crowell Nov 18 '17 at 1:24
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Have you really performed the experiment with riding a bicycle past a music source? I do not know with what speed you can ride your bicycle, but with a generous assumption of $10$m/sec, I arrive at the frequency distortion of $1.03$. This is less than half-tone (the ratio of the frequencies of two neighboring piano keys (black and white). So I imagine that "an ancient" standing and listening how a horseman riding past him at a full speed sounds a horn will not notice much difference. To have this $1.03$ frequency change, the horseman has to ride straight at you; if he passes you at some distance, the effect will not be sharp but gradual. And the horseman has to produce the same note on his horn, continuously. So I doubt that this was noticed.

By the way Doppler himself discovered the effect by observing light, rather than sound. (Railroads already existed in 1842 when the effect was discovered. One can easily hear the Doppler effect when a train on full speed passes you while sounding the signal).

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    $\begingroup$ I would say Doppler identified the effect. Rather as everyone knew apples fell to the ground before Newton, folks certainly heard pitch-changes as railroad trains went by, but didn't stop to derive the physics behind the effect. $\endgroup$ – Carl Witthoft Nov 17 '17 at 15:56
  • $\begingroup$ I notice Doppler shifts all the time when people ride a bike past me while I'm out running on my city's trail system. (Some cyclists have music players that they listen to while riding.) It is not subtle at all. Note that your calculation is off by a factor of two if someone passes by on a bike. There is an upward shift of 3% while they approach, and a downward 3% as they recede, so the difference we hear is 6%. And frequency shifts of much less than a half-tone are easily noticeable to someone with musical training $\endgroup$ – Ben Crowell Nov 18 '17 at 1:22
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    $\begingroup$ It's still pure speculation that an ancient Greek (for example) would notice the effect from someone riding past full gallop on a horse. A galloping horse makes quite a racket! And the rider wouldn't have a music player. Short of some documentary evidence, I'm skeptical about any ancient observations of the Doppler effect. $\endgroup$ – Michael Weiss Nov 20 '17 at 0:58
  • $\begingroup$ @CarlWitthoft Railroad trains did not go by until 19th century, and the effect was scientifically described soon after, in 1845. $\endgroup$ – Conifold Nov 20 '17 at 19:11

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