Sound wave and Principle of relativity

Question

Principle of Relativity:

"An experimenter doing an experiment in an inertial frame of reference can never measure the velocity of its own frame of reference. OR a law of physics is never expressed (can never be expressed) in terms of the speed of the inertial reference frame in which it is valid".

This is a very general principle and should be applicable across all domains of physics. It was first stated by Galileo and then preserved by Einstein in Special theory of relativity. Einstein's second postulate "Constancy of speed of light in all inertial frame of reference" supports this principle of relativity. The speed of light is always $c$ (no more no less) when measured in all inertial reference frames and hence no body can find the velocity of his own frame of reference by measuring speed of incoming light. So far so good.

Sound wave have one similarity with light waves. Their velocities do not depend on the velocity of their sources. But velocity of sound unlike velocity of light do depend on the velocity of inertial reference frame of the listener. $$\text{Observed sound velocity:}\quad V(\text{measured}) = V(\text{sound}) +/- V(\text{listener}) \;.$$ So an observer or listener can determine its own velocity by measuring the velocity of sound (since we know that $V(\text{sound}) = 330 \,\text{meters/second}$).

So, is this not violation of principle of relativity?

Answer 1

Physical law gives the speed of most waves (including sound) relative their medium. And that relative velocity remains correct for observers at rest relative the medium or in motion relative the medium.

So the principle of relativity is preserved.

That is the reason Einstein added a special postulate to indicate that the observed speed of light was the same for all observer rather than relying on the first postulate to cover it: most wave phenomena are understood to occur in a medium and therefore get treated in terms of the medium. Light is an exception to an otherwise very broad rule.

Answer 2

I got the required hint from dmckee's answer to my question. I think that now I understand it properly. So I felt a need to write a detailed answer.

This discussion in the context of velocity of sound actually describes the Galilean or pre-STR restricted meaning of the Principle of relativity.

Sound waves appear to propagate at a different velocity in any inertial frame which is moving with respect to the air. However, this does not violate the relativity principle, since if the air were stationary in the second frame then sound waves would appear to propagate at 330 meters per second in this frame as well.

Mechanical waves velocities are exclusively defined in those frames of reference in which their material medium is at rest. In those frames of reference, the velocity of the wave is a constant irrespective of velocity of the source. Any experiment done in a frame of reference in which the material medium is at rest, can never determine the speed of that frame of reference. For example, if an experimenter measures the speed of sound in a frame of reference where the medium "air" is at rest, he would always measure the speed of sound as 330m/s. This is actually the “pre STR” beliefs or in a sense “restricted beliefs” of the Principle of relativity. Einstein stated by his postulates that the Principle of relativity is more wide spread and more general than what Galileo and Newton believed it to be.

Answer 3

You are missing a couple of important points, as did the author of the version of the principle of relativity you quoted.

Firstly, velocity is a relative property. As you sit reading this answer you do not have a single velocity- you have any number of them. Relative to your chair, you might be stationary. Relative to a passing car, or helicopter or satellite you might be moving at tens or thousands of miles per hour. You can never have an absolute velocity.

Secondly, the opening sentence of the principle of relativity you quoted is hopelessly ambiguous, and certain interpretations of it are simply untrue. If, for example, I am cycling down your street, I can perform an experiment in my frame of reference (ie the set of coordinates in which I am at rest) to measure my speed relative to the street, so in that sense the sentence in question is patently false.

However, imagine you are in an enclosed railway carriage. If you measure the speed of sound in the carriage, you will not be able to tell from that measurement alone whether the carriage is moving relative to the air outside.

The principle of relativity means that all inertial reference frames are equivalent as far as the laws of physics are concerned. That means that if you perform an experiment in one inertial reference frame, you will obtain exactly the same result of you then perform exactly the same experiment in another reference frame. By 'exactly' the same I mean exactly in every sense. Clearly if I measure the speed of the wind by standing on the ground holding an anemometer, and then repeat the experiment on a motorbike at 100m/s, I will get different answers because I am not performing exactly the same experiment.