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The intensity of a sound wave is dependent upon pressure amplitude squared. Consider a source of power P emitting sound in all directions. An observer moving with a speed v towards the source will not see any change in the pressure amplitude. This shows that intensity of sound wave heard by observer would be the same as a stationary observer, but this is definitely wrong, as more sound energy is incident on moving observer for same time duration as more wavefront pass through it.

Where am I conceptually wrong about intensity of sound waves and what is the correct formula for observed intensity for a moving observer?

Thank you.

Shridp
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1 Answers1

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One misconception here seems to be that pressure perturbations must increase to increase the flux of acoustic energy reaching the moving observer. The fact that the observer moves towards the source means that the time for some amount of acoustic energy to reach the observer will differ from the time during which it was emitted by a factor of $1 - \frac{v}{c}$ (where $c$ is the sound speed). Energy per volume stays the same (pressure amplitude does not increase) but the flux passing through a surface will be increased when that surface moves towards the source.

FTT
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