If the observer moves with a velocity of magnitude v_o (relative to the air) then the velocity of the waves relative to the observer is (v±v_o).

In this case the wavelength of the waves is unchanged.

Therefore the apparent frequency is now given by

It should be clear that, in the case where both source and observer are moving, if v_s and v_o are equal, then f’ = f. In other words, the Doppler effect depends on the relative velocity of source and observer (as stated above).

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