Answer to Question #218999 in Physics for ran li

Question

An automobile is approaching you at a speed of 50.0 km/h and sounding its horn. The fundamental frequency of the horn sounds to you like 266 Hz. If the speed of sound is 335 m/s, the real fundamental frequency of the horn is ___Hz. (Give your answer with the correct number of sig digs and do not include units)

Answer 1

We can find the real fundamental frequency of the horn from the Doppler Shift formula:

$$f_o=f_s(\dfrac{v}{v-v_s}),$$ $$f_s=\dfrac{f_o}{\dfrac{v}{v-v_s}}=\dfrac{f_o(v-v_s)}{v},$$ $$f_s=\dfrac{266\ Hz\cdot(335\ \dfrac{m}{s}-13.88\ \dfrac{m}{s})}{335\ \dfrac{m}{s}}=255\ \dfrac{m}{s}.$$