Question

A source emitting a frequency of 480 Hz is moving toward a stationary observer. If the frequency heard by the observer is 560 Hz, what is the speed of the source? Assume a sound speed of 345 m/s.

Answer 1

The emitted $f_0 = 480Hz$ and received $f=560Hz$ frequencies are connected with the following formula (see Doppler effect):

$$f = f_0\dfrac{1}{1-\dfrac{v}{c}}$$

where $c = 545m/s$ is the sound speed, and $v$ is the speed of the source with respect to the medium. Thus, expressing $v$, obtain:

$$v = c\left(\dfrac{1-f_0}{f} \right)\\ v = 545m/s\left(1- \dfrac{480Hz}{560Hz}\right) \approx 77.9m/s$$

Answer. 77.9 m/s.