Question

Unless specifically stated otherwise, you may assume the speed of sound for all the scenarios below is 350 m/s.2.A traffic cop uses a sonar gun to check for speeding cars. The sonar gun emits a sound wave with a frequency of 35,000 Hz. The sonar waves are reflected by the oncoming cars and are read by the gun’s receiver. For one car coming towards the traffic cop, the sonar gun reads a frequency of 37,700 Hz. How fast is the oncoming car moving?

Answer 1

We have the following data:

fo: frequency observed; fo = 37700 Hz

fs: actual frequency emitted; fs = 35000 Hz

vo: velocity of observer; vo = 0 m/s

v: velocity of sound; v = 350 m/s

We need to solve for the velocity of the car, so let's call that vs.

Doppler effect equation:

fo/fs = (v+vo)/(v+vs)

Now let's substitute all the variables we know:

37700/35000 = (350+0)/(350+vs)

Let's isolate vs:

350+vs = 35000(350)/37700

vs = 35000(350)/37700 - 350

vs = -25.066 m/s

Since velocity of the car is negative in relation to the cop, this means the car is approaching the cop. Its speed is |vs| = 25.066 m/s