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 1310 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 1240 Hz.

What is the frequency of the siren in the police car?
The speed of sound in air is 343 m/s.

a) 1320 Hz
b) 1300 Hz
c) 1370 Hz
d) 1360 Hz
e) 1270 Hz

Answer 1

The frequency of the siren in the police car is f=1277.6 Hz.

Step-by-step explanation:

The frequency percibed by a receptor wich is in movement with an emisor moving too, is given by

`f^(')=f(v+v_(r))/(v-v_(f))` if the emisor is approaching and

`f^('')=f(v-v_(r))/(v+v_(f))` if the emisor is moving away from the receptor.

Where
`f^(')` is the frequency when approaching,
`f^('')` the frequency when moving away,
`v` is the speed of sound,
`v_(r)` is the velocity of the receiver, and
`v_(f)` is the velocity of the emisor (wich we don't know in advance). From the second equation we clear
`v_(f)` and put it in the first equation, obtaining

`f=(1310*2*343)/(343+35)*(1)/(1+(1310)/(1240)*(343-35)/(343+35))`

thus

`f=1277.6 Hz`

is the frequency of the siren in the police car.