# Sound wave and Principle of relativity

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?

• It is also worth noting that the speed of a sound wave (or any other wave in a medium) relative the source depend on the motion of the source in exactly the same fashion that the speed relative the receiver does. And the speed relative the medium depends on neither. There is a symmetry here that is not exposed in the way you stated it. – dmckee --- ex-moderator kitten Jul 12 '19 at 20:31
• I am trying hard to understand your concept. "speed of a sound wave (or any other wave in a medium) relative the source depend on the motion of the source"--their is no dependence......" in exactly the same fashion that the speed relative the receiver does"---observed speed of sound depends on the speed of the observer. So where am I missing the point? – user103515 Jul 14 '19 at 17:21
• The speed (or velocity) of a wave in a medium can be measured by noting the position of a particular feature of the wave as a function of time. You can measure a speed in this way whether you are at rest relative the medium or not. But (with the sole exception of light) the speed set by the wave mechanism is the speed measured by on observer at rest relative the medium. Walk along the shore by a pond and throw in a pebble: the wave moving in the direction of your walking will move more slowly relative you than the ones going backward. – dmckee --- ex-moderator kitten Jul 14 '19 at 19:40

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.

• "And that relative velocity remains correct for observers at rest relative the medium 'or in motion relative the medium' ". I could not understand the "or in motion relative the medium". As I have mentioned in the question; V(of sound observed by observer in relative motion with the medium)= V(of sound relative to medium)+/-V(of Observer relative to medium). So where am I missing the point. Please explain. – user103515 Jul 14 '19 at 17:33

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.

Matter waves 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.