Answer to Question #219000 in Physics for ran li

Question

An automobile is approaching you at a speed of 90.0 km/h and sounding its horn. The fundamental frequency of the horn sounds to you like 268 Hz. If the real fundamental frequency of the horn is 248 Hz, the speed of sound is ___m/s. (Give your answer with the correct number of sig digs and do not include units.

Answer 1

We can find the speed of sound from the Doppler Shift formula:

$$f_o=f_s(\dfrac{v}{v-v_s}),$$ $$v=\dfrac{f_ov_s}{(f_o-f_s)},$$ $$v=\dfrac{268\ Hz\cdot25\ \dfrac{m}{s}}{(268\ Hz-248\ Hz)}=335\ \dfrac{m}{s}.$$