Question

Two train whistles have identical frequencies of 180 Hz. When one train is at rest in the station, sounding its whistle, a beat frequency of 3.7 Hz is heard from a train moving toward us. Find the speed of the train. (Take the speed of sound to be 345 m/s.)

Answer 1

7 m/s

Explanation:

We are given that

Frequency at stationary =
`f_0=180Hz`

Beat frequency=3.7 Hz

Apparent frequency=
`f=180+3.7=183.7Hz`

Speed of sound=v=345 m/s

We have to find the speed of train

Apparent frequency=
`f=f_0((v)/(v-v_s))`

Substitute the values then we get

`183.7=180((345)/(345-v_s))`

`345-v_s=(180* 345)/(183.7)`

`345-v_s=338`

`v_s=345-338=7 m/s`

Hence, the speed of train=7 m/s