Question

a car travelling south at 36 m/s sounds a 456 hz horn . what frequency is heard by the driver in an approaching truck traveling north at 25 m/s? what frequency is heard by the driver if he is heading south away from the car at 25 m/s?

Answer 1

a) We can find the frequency which is heard by the driver in the approaching truck from the Doppler Shift formula:

$$f_o=f_s\dfrac{v+v_o}{v-v_s},$$

here, $f_o$ is the frequency which is heard by the driver in the approaching truck, $f_s=456\ Hz$ is the source frequency, $v=340\ \dfrac{m}{s}$ is the speed of the sound, $v_s=36\ \dfrac{m}{s}$ is the speed of the source (or the car), $v_o=25\ \dfrac{m}{s}$ is the speed of the observer (or the speed of the driver in the truck).

Then, we get:

$$f_o=456\ Hz\cdot\dfrac{340\ \dfrac{m}{s}+25\ \dfrac{m}{s}}{340\ \dfrac{m}{s}-36\ \dfrac{m}{s}}=547.5\ Hz.$$

b) We can find the frequency which is heard by the driver in the truck if he is heading south away from the car from the Doppler Shift formula:

$$f_o=f_s\dfrac{v-v_o}{v-v_s},$$

here, $f_o$ is the frequency which is heard by the driver in the truck heading south away from the car, $f_s=456\ Hz$ is the source frequency, $v=340\ \dfrac{m}{s}$ is the speed of the sound, $v_s=36\ \dfrac{m}{s}$ is the speed of the source (or the car), $v_o=25\ \dfrac{m}{s}$ is the speed of the observer (or the speed of the driver in the truck).

Then, we get:

$$f_o=456\ Hz\cdot\dfrac{340\ \dfrac{m}{s}-25\ \dfrac{m}{s}}{340\ \dfrac{m}{s}-36\ \dfrac{m}{s}}=472.5\ Hz.$$

Answer:

(a) $f_o=547.5\ Hz.$

(b) $f_o=472.5\ Hz.$