Question

A car travelling south at 36 m/s sounds a 456 Hz horn.

(a) What frequency is heard by the driver in an approaching truck traveling north at 25 m/s?

(b) What frequency is heard by the driver if he is heading south away from the car at 25 m/s?

Answer 1

(a) From the Doppler Shift formula

$f=f_s\cdot\frac{v+v_0}{v-v_s}=456\cdot\frac{340+25}{340-36}=547.5\ (Hz)$

$v$ - is the speed of the sound;

$v_0$ - is the speed of the observer;

$v_s$ - is the speed of the source;

$f_s$ - is the source frequency.

(b) From the Doppler Shift formula

$f=f_s\cdot\frac{v-v_0}{v-v_s}=456\cdot\frac{340-25}{340-36}=572.5\ (Hz)$