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)

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

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

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

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

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