Question

You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind and you perceive the frequency as 1370 Hz. You are relieved that he is in pursuit of a different speeder when he continues past you, but now you perceive the frequency as 1330 Hz. What is the speed of the police car? The speed of sound in air is 343 m/s.

Answer 1

Answer:

Explanation:

Given

Apparent  frequency $f'=1370\ Hz$

Velocity of sound $v=343\ m/s$

speed of observer $v_o=35\ m/s$

Using Doppler effect Apparent frequency when source is approaching is given by

$f'=f(\frac{v-v_0}{v-v_s})$

$1370=f(\frac{343-35}{343-v_s})---1$

Apparent frequency when source moves away from observer

$f''=f(\frac{v+v_0}{v+v_s})$

$1330=f(\frac{343+35}{343+v_s})---2$

Divide 1 and 2 we get

$\frac{f'}{f''}=\frac{\frac{343-35}{343-v_s}}{\frac{343+35}{343+v_s}}$

$\frac{1370}{1330}=\frac{343-35}{343-v_s}\times \frac{343+v_s}{343+35}$

$v_s=40\ m/s$

Thus speed of sound of police car is 40 m/s