Question

A person watches an ambulance drive by them while emitting a steady sound from its siren. When the ambulance passes the person (switching from moving towards him to moving away from him), the perceived frequency of the sound he receives decreases by 11.2 percent. How fast is the ambulance driving

Answer 1

Answer:

21.7 m/s

Explanation:

Let the velocity of ambulance is v and f is the real frequency of siren of ambulance.

the velocity of sound is 343 m/s

use the formula of Doppler's effect

$f' = \frac{343}{343-v}f$    .... (1)

where, f' is the frequency of at the first time.

Now the source is moving away from the person, the frequency is given by

$f'' = \frac{343}{343+v}f$    .... (2)

According to the question,

f'' = f' - 11.0 % of f'

f'' = 0.881 f'

By equation (1) and (2)

$\frac{343}{343+v}f= \frac{343}{343-v}\times 0.881f$

40.817 = 1.881 v

v = 21.7 m/s

Thus, the speed of ambulance is 21.7 m/s.