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

Answer:

7 m/s

Step-by-step 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=$f=f_0(\frac{v}{v-v_s})$

Substitute the values then we get

$183.7=180(\frac{345}{345-v_s})$

$345-v_s=\frac{180\times 345}{183.7}$

$345-v_s=338$

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

Hence, the speed of train=7 m/s