Question

An alert physics student stands beside the tracks as a train rolls slowly past. He notes that the frequency of the train whistle is 496 Hz when the train is approaching him and 478 Hz when the train is receding from him. Using these frequencies, he calculates the speed of the train. What value does he find? (Assume the speed of sound in air is 343 m/s.)

Answer 1

6.455 m/s

Step-by-step explanation:

Given;

Frequency of train whistle, f = 496 Hz

Frequency observed, f' = 478 Hz

Speed of sound in air = 343 m/s

Now,

From the instant Doppler's effect, we have the relation

`f = (v+v_s)/(v-v_s)* f'`

here,

v is the speed of the sound

`v_s` is the speed of the train

`496 = (343+v_s)/(343-v_s)*478`

or

1.037 × ( 343 -
`v_s` ) = 343 +
`v_s`

or

355.91 -
`v_s` = 343 +
`v_s`

or

12.91 =
`2v_s`

or

`v_s` = 6.455 m/s