Question

A frequency of 485 Hz is being emitted from a source moving at 68.9 m/s away from a stationary observer. What frequency is heard by the observer? (Assume the speed of sound to be 343 m/s)

Answer 1

We can find the frequency heard by observer from the Dopler shift formula:

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

here, $f_o$ is the frequency heard by observer, $f_s = 485 \ Hz$ is the frequency emitted by the source, $v =343 \ \dfrac{m}{s}$ is the speed of sound, $v_0 = 0 \ \dfrac{m}{s}$ is the speed of the observer, $v_s = 68.9 \ \dfrac{m}{s}$ is the speed of source, the top sign is for the source approaching the observer and the bottom sign is for the source departing from the observer.

Then, we can rewrite the formula and calculate $f_o$ :

$$f_o = f_s \dfrac{v}{v + v_s} = 485\ Hz \cdot \dfrac{343 \ \dfrac{m}{s}}{343 \ \dfrac{m}{s} + 68.9 \ \dfrac{m}{s}} = 404 \ Hz.$$

Answer:

$f_o = 404 \ Hz.$