Doppler shift vs. Galilean relativity?

Question

When the source of sound is moving away from a receiver, the formulas for the Doppler shift are different when the source is moving then when the receiver is moving. How is this reconciled with the Galilean relativity which holds that all velocities are relative and the physics is independent of which frame of reference is used to describe the events ( such as the rate of which the source and receiver are approaching each other is the same in both frames of reference)?

Answer 1

The physics of the Doppler effect depend not just on the relative speed between source and receiver, but also on their speeds relative to the sound medium (the air). Since the speed of sound is measured relative to a stationary medium, the Doppler equations are expressed in a reference frame in which medium is stationary. This is what breaks the symmetry. In the case where the source is moving, the receiver is stationary with respect to the medium; which means a pulse from the source reaches the receiver in time t = distance/v_sound. On the other hand, in the case where the RECEIVER is moving (receding), the receiver is IN MOTION with respect to the medium. In this case a pulse from the source reaches the receiver in time t = distance/(v_sound-v_receiver); it is essentially as if the speed of sound (relative to the receiver) has slowed down in this case. This means the two situations are not symmetrical.



It's worth noting that the Doppler equations for LIGHT are different than for sound. Light does not require a medium, so the concept of speeds relative to the medium is meaningless. The Doppler equations for light ARE symmetrical, whether the source or receiver is considered to be "moving".

Answer 2

"Doppler shift vs. Galilean relativity?"



Pretty much, this cannot be reconciled, since the "ships' cabin" is sealed. So if you hear the pitch go up and then down, you know you passed the source. But you cannot infer speed from Doppler shift, because the measurement does not occur in your ship's cabin. You have to *assume* something about the emitting process, and wind speed.



"When the source of sound is moving away from a receiver, the formulas for the Doppler shift are different when the source is moving then when the receiver is moving."



Or when there is a strong wind...



"How is this reconciled with the Galilean relativity which holds that all velocities are relative and the physics is independent of which frame of reference is used to describe the events ( such as the rate of which the source and receiver are approaching each other is the same in both frames of reference)?"



It doesn't. Thanks for asking.

Answer 3

Galileo was correct for the time and the state of scientific knowledge at the time. But that was 200 years or more before Doppler and his experiments.



But what Galileo said was that two observers moving relative to each other would get the same experimental results as each other *in their respective frames of reference*.



You are carrying this further to compare results between *different* frames of reference. That is not what Galileo said.



There isn't enough space to go into details here. You can find more than enough with a simple search on the internet. But you are talking about observations made by someone in a different frame of reference to that of the sound emitter. In fact, since sound requires some sort of medium to propogate in, there is a third potential frame of reference to consider - that of the air through which it travels.



It is an undisputed fact that the stationary obvserver hears a frequency which is different from that emitted by the moving source. But, once corrected for the observed motion of the source, the stationary observer will be able to accurately determine the frequency of the source, and it will agree with the frequency determined by someone travelling with the source. In other words, observations made in the different frames of reference CAN agree on the results, although the two sets of observations can be different. But, again, this is not what Galileo was talking about.

Answer 4

Doppler works only for Relative Motion between the source and the Receiver.



====> If you were in a sealed rail car moving at constant velocity on vibrationless tracks, you could not use a MP3 Player with speakers at the end of the car to determine if the car was moving.



The MP3 player would have to be sitting on the ground next to the tracks.