Answer to Question #161979 in Optics for Tony

Question

If a 1.00kHz sound source moves at a speed of 50.0m/s toward a listener who moves at a speed of 30.0m/s in a direction away from the source, what is the apparent frequency heard by the listener? The speed of sound in air is 343m/s.

Answer 1

Applying the formula for the Doppler effect, obtain the observed frequency:

$$f = \dfrac{c - v_l}{c - v_s}f_0$$

where $c = 343 m/s$ is the speed of soung, $v_l = 30m/s$ is the speed of the listener, $v_s = 50m/s$ is the speed of the source, and $f_0 = 1kHz$ is the natural frequency of the source. Thus, find

$$f = \dfrac{343m/s - 30m/s}{343m/s - 50m/s}\cdot 1kHz \approx 1.068\space kHz$$

Answer. 1.068 kHz.