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We know the basic formula of apparent frequency in Doppler's effect :

$$\mathrm{f'=\frac{v_{sound}\pm v_{observer}}{v_{sound}\pm v_{source}}}f$$

  • What do we do when the medium itself is moving, say with a speed $u$?
  • Are the velocities in the above formula with respect to the medium frame or ground frame?
  • If not, then what do we do?

I know that the medium, if moving along the direction of sound propagation will increase the sound velocity. But how can we use this fact in the formula?

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  • In the formula $f'=\frac{v_{sound}\pm v_{observer}}{v_{sound}\pm v_{source}}f$ expressing the Doppler effect, $v_{sound}$ is the speed of the waves (sound in this case) in the medium (this quantity is independent of the speed of the medium), while $v_{observer}$ and $v_{source}$ are speeds of the observer and source measured with respect to the medium. Further, the positive and negative signs in the formula depend on the direction of relative velocity of the source and observer. Please see the linked wiki article for a more detailed verbal description.
  • The speeds of the source and observer in the formula are measure relative to the medium.

Note that there is indeed an inverse Doppler effect which occurs in media with negative refractivity, and is a topic of ongoing research.

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