Speed of a sound wave (compressibe flow)

[xJJx]

Hi, there is no particular question that I need help on, just something my lecturer told us in lesson which I couldn't quite understand so i'd like to check my understanding on this. I know that the speed of a soundwave is 'c' in undisturbed flow. Suppose the flow velocity is 'U'. If the soundwave is convected by the flow, would the resultant velocity of the soundwave be 'c + U' if the wave is traveling in the same direction as flow, and would it be 'c - U' (vector sum) if the wave is traveling in the opposite direction to the flow? Does the centre of the sound wave travel at a speed of U whilst the ripples propagate at speed c?
Also, my teacher said that at Mach 1, the speed of the sound wave is exactly 0, which is why the soundwaves stop and compile to form a shockwave. I don't understand how the speed can be 0 when U=c at mach 1.
thank you!

 

[anorlunda]

All motion is relative. The Earth is moving through space as you speak. How do you handle that. When you talk on an airplane, how do you handle that?

 

[scottdave]

The "Sonic boom" is experienced by an outside observer. The source of the sound (a jet plane, for example) is moving at Mach 1. The medium (air) through which the sound travels is not moving at Mach 1

 

[jack action]

would the resultant velocity of the soundwave be 'c + U' if the wave is traveling in the same direction as flow, and would it be 'c - U' (vector sum) if the wave is traveling in the opposite direction to the flow?

Yes.

Does the centre of the sound wave travel at a speed of U whilst the ripples propagate at speed c?

Yes.

Also, my teacher said that at Mach 1, the speed of the sound wave is exactly 0, which is why the soundwaves stop and compile to form a shockwave. I don't understand how the speed can be 0 when U=c at mach 1.

The speed is not zero. It is zero relative to the sound source since they travel at the same velocity (only considering the moving direction of the sound source). So, as soon as the sounds source emits a sound wave, it "follows" it since they travel at the same velocity. When the sound source emits another sound wave, it therefore "stacks" on the previous sound wave.

 

[boneh3ad]

The bottom line is you just have to remember that sound travels at the speed of sound $c$ (sometimes written as $a$ as well) relative to the air, so if the air is moving, you have to take that into account if you are looking at the wave speed relative to a stationary observer.

 

[xJJx]

Yes.

Yes.

The speed is not zero. It is zero relative to the sound source since they travel at the same velocity (only considering the moving direction of the sound source). So, as soon as the sounds source emits a sound wave, it "follows" it since they travel at the same velocity. When the sound source emits another sound wave, it therefore "stacks" on the previous sound wave.

View attachment 236279​

Thank you so much! this was very helpful. It creeps up a lot in exam questions so it's worth knowing

 

[xJJx]

The bottom line is you just have to remember that sound travels at the speed of sound $c$ (sometimes written as $a$ as well) relative to the air, so if the air is moving, you have to take that into account if you are looking at the wave speed relative to a stationary observer.

thank you!