Question

A source passing a stationary observer is emitting a frequency of 560 Hz. If the speed of sound is 345 m/s, what must the speed of the source be if the frequency of the source is 480 Hz? (Ans: 58 m/s)

Answer 1

The Doppler's effect says

$$f=f_0\frac{c\pm v_r}{c\pm v_s}$$

$$f=f_0\frac{c}{c+ v_s}$$

$$v_s=c(f_0/f-1)\\ =345(560/480-1)=58\:\rm m/s$$