Question

The horn on a commuter train emits sound with a frequency of 342.5 Hz when the train is at rest. The train sounds its horn as it passes a passenger platform at a constant speed of 41 m/s. What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding? Remember that change of frequency means the final frequency minus the initial frequency. Be sure to include the correct sign on the answer. (Take the speed of sound to be 345 m/s.)

Answer 1

Δf = -82.57 Hz

Step-by-step explanation:

For this problem we will use Doppler effect formula:

`f = (C+Vr)/(C+Vs)*fo` where:

C is the speed of sound

Vr is the velocity of the person = 0m/s

Vs is the velocity of the source (train): When approaching Vs = -41m/s and when receding Vs = 41m/s

fo = 342.5 Hz

When the train is approaching:

`fa = (C)/(C+Vs)*fo = (345)/(345-41)*342.5=388.69Hz`

And when the train is receding:

`fr = (C)/(C+Vs)*fo = (345)/(345+41)*342.5=306.12Hz`

So, the change of frequency will be:

Δf = fr - fa = 306.12 - 388.69 = -82.57 Hz