# Does the speed of sound depend on the observer's relative motion?

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1. Oct 23, 2014

### GenlyAi

Hi,
I wanted to ask if the speed of a sound wave, given a fixed medium, depends on the speed of the observer. That is to say, does the speed of sound obey to the laws of relative motion, implying addition of relative speeds? In case it doesn't depend on relative motion, can you explain why? I know that the Doppler effect accounts for the speed of the observer, but it only affects the frequency of the wave, not its speed. Why is it so (in case it actually is)?
Thanks.

2. Oct 23, 2014

### phinds

Yes it does. Unlike light, sound adds/subtracts "normally". The "Doppler Effect" applies equally well to both source and observer. There would be no difference between a tuning fork on a moving train heard by an observer at the station vs the same tuning fork on the station heard by someone on the train. The situations are symmetric because motion is relative.

3. Oct 23, 2014

### A.T.

The speed is fixed relative to the medium, so it depends on the velocity of the observer relative to the medium, and the propagation direction. in frames where the medium moves, the propagation speed is anisotropic.

Last edited: Oct 23, 2014
4. Oct 23, 2014

### A.T.

Wrong. There would a difference in the heard frequency. See the two
different formulas for movement of the source vs. movement of the receiver relative to the medium:
http://en.wikipedia.org/wiki/Doppler_effect#Analysis

The relativity of motion
implies symmetry for 2 objects. But here you have 3: source, receiver and medium.

5. Oct 23, 2014

### phinds

Interesting. Thanks.

6. Oct 24, 2014

### GenlyAi

Thank you for your answers. So , if the speed of sound is relative, can you provide a formula or equation showing its dependence on the speed of the source and/or of the observer? I wasn't able to find it on the Internet. In other words, the usual definition $c = \sqrt{\frac{K}{\rho}}$ doesn't include the speed of the source or observer or both. It's like as if it is a definition for the speed of sound for a source at rest, but this is never specified. It would be like, for example, omitting the dependence on the acceleration when giving the general equation of motion for x: $x = x_0 + vt + \frac{1}{2}at$. That would be a special case where a = 0.

7. Oct 24, 2014

### A.T.

Not for source at rest, but for medium at rest. If the medium moves, vector addition determines propagation velocities in different directions.