Question

A fire engine is being driven away from you at a speed of 15.4 m/s. One of the notes in its siren sequence has a fundamental frequency of 244 Hz. If the speed of sound is 338 m/s, the fundamental frequency of that particular note will seem to you to be ___Hz. (Give your answer with the correct number of sig digs and do not include units)

Answer 1

We can find the observed fundamental frequency of that particular note from the Doppler Shift formula:

$$f_o=f_s(\dfrac{v}{v+v_s}),$$ $$f_o=244\ Hz\cdot(\dfrac{338\ \dfrac{m}{s}}{338\ \dfrac{m}{s}+15.4\ \dfrac{m}{s}})=233\ Hz.$$