Question

A car's horn produces a frequency of 440 Hz at rest.If the car is traveling east at 20 m/s towards an observer, what speed and direction (E or W) must an observer have to hear a frequency of 450 Hz?

Answer 1

Now Using Doppler's effect:

When observer and source are moving towards the observer, then frequency is given by:

f1 = f0*(Vs + Vo)/(Vs - Va)

Here given that:

Vs = Speed of sound = 343 m/sec

f0 = frequency of stationary source = 440 Hz

Va = Speed of car = 20 m/sec

Vo = Speed of observer = ? m/sec

f1 = observed frequency = 450 Hz

So Using these values:

450 = 440*(343 + Vo)/(343 - 20)

343 + Vo = 450*(343 - 20)/440 = 330.34

Vo = 330.34 - 343 = -12.66 m/sec

-ve sign means observer is moving away from the source towards east

Speed of observer = 12.66 m/sec

Direction = towards west