Question

An observer measures a 100 Hz Doppler shift as an ambulance goes by. At rest, the frequency of the ambulance's siren is 2,000 Hz. What is the speed of the ambulance?

Answer 1

The change in the frequency of the sound, due to the relative motion of the source of sound and the observer, is determined by the Doppler's Effect.

The speed of the ambulance (source) is "6517 m/s"

The equation of Doppler's Effect is given as follows:

$f_o = \frac{v+v_o}{v+v_s}f_s$

where,

$f_o$ = frequency of sound measure by observer  = 100 Hz

v = speed of sound = 343 m/s

$v_o$ = speed of observer = 0 m/s

$v_s$ = speed of ambulance (source) = ?

$f_s$ = actual frequency = 2000 Hz

Therefore, using the values, we get:

$100\ Hz = \frac{343\ m/s + 0\ m/s}{343\ m/s + v_s}(2000\ Hz)\\\\(100\ Hz)(343\ m/s + v_s) = (343\ m/s)(2000\ Hz)\\\\v_s = \frac{686000\ Hz.m/s - 34300\ Hz.m/s}{100\ Hz}$

v_s = 6517 m/s

Learn more about Doppler's Effect here:

brainly.com/question/1330077?referrer=searchResults