Speed of a sound wave (compressibe flow)

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The speed of a sound wave in undisturbed flow is denoted as 'c', while the flow velocity is 'U'. When a sound wave travels in the same direction as the flow, its resultant velocity is 'c + U', and in the opposite direction, it is 'c - U'. At Mach 1, the speed of the sound wave is considered zero relative to the sound source because both travel at the same velocity, causing sound waves to stack and form a shockwave. Understanding that sound travels at speed 'c' relative to the air is crucial, especially when considering the motion of the medium. This concept is important for exam preparation and practical applications in compressible flow.
xJJx
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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!
 
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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
 
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xJJx said:
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.
xJJx said:
Does the centre of the sound wave travel at a speed of U whilst the ripples propagate at speed c?
Yes.
xJJx said:
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.

speed%2Bof%2Bsound.jpg
 

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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.
 
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jack action said:
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.

Thank you so much! this was very helpful. It creeps up a lot in exam questions so it's worth knowing
 
boneh3ad said:
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!
 
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