Does the velocity of sound change when the source moves?

[Hamal_Arietis]

Homework Statement

Will the velocity of sound change if the source moves?

Homework Equations

The velocity of velocity of sound in air equals:
$$V=\sqrt{\frac{\gamma RT}{M}}=const$$

The Attempt at a Solution

I think it doesn't change. But it seems to conflict with the equation :
$$\vec{v_{air}}=\vec{v_s}+\vec{V}$$

 

[haruspex]

Homework Statement

Will the velocity of sound change if the source moves?

Homework Equations

The velocity of velocity of sound in air equals:
$$V=\sqrt{\frac{\gamma RT}{M}}=const$$

The Attempt at a Solution

I think it doesn't change. But it seems to conflict with the equation :
$$\vec{v_{air}}=\vec{v_s}+\vec{V}$$

Please explain what each velocity represents in that last equation.

 

[Hamal_Arietis]

In room reference frame
$v_{air}$ is the velocity of sound that observer receives. $v_s$ is velocity of source and $V$ is the velocity of sound if source doesn't move.

 

[haruspex]

In room reference frame
$v_{air}$ is the velocity of sound that observer receives. $v_s$ is velocity of source and $V$ is the velocity of sound if source doesn't move.

I don't understand.
In the room reference frame, the source, receiver and air may all have a velocity, and the sound has a velocity relative to the air.
Let's call these v_s, v_r, v_a, and V respectively, all measured in the same direction.

What does your equation look like in those terms? You seem to be saying that the sound arrives at the receiver with speed V+v_s-v_r, but that is not true. No matter how the source moves, the velocity of the sound waves relative to the room is V+v_a, and relative to the receiver is V+v_a-v_r. The frequency is another matter.

 

[Hamal_Arietis]

Sorry .I seem air and receiver don't move. And source comes near observer. So the velocity of sound that obsever receives v=vs+ V

 

[haruspex]

Sorry .I seem air and receiver don't move. And source comes near observer. So the velocity of sound that obsever receives v=vs+ V

No, as I posted, the velocity of the source does not affect the velocity of the sound waves. It does affect the frequency.

 

[Hamal_Arietis]

Thanks a lot for helping. I understanded.
Answering this question helps me prove the Dopper effect.