Apparent frequency of sound emitted by a moving source

A point source moves at a constant velocity vS from S0 to S in a time t. Figure 7.15 shows the positions of wavfronts W0 (emitted from the source when at S0), and W1 and W2 (emitted at equal intervals of time as the source moves from S0 to S.)


Figure 7.15 Doppler effect for a moving source.

The waves reaching an observer in front of the source are compressed into the distance S2X = (v - vS) t and we can calculate their wavelength as folows:

The speed of sound v is constant, so f 1 = f' 1, giving 1 = f1

Substituting for X' from Equation (7.3) -

If the source is moving away from the listener at the same speed, f' = ——— .

Non-mathematical reasoning gives the same results, that the frequency is higher when the source and the observer approach each other and lower when they move away from each other.

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