One train is approaching an observer at rest and another train is receding from him with the same velocity `4 m//s` . Both trains blow whistles of same frequency of `243 H_(Z)` . The beat frequency in `H_(Z)` as heard by observer is (speed of sound in air = `320 m//s`)

Options

A. 10
B. 6
C. 4
D. 1

Answer

B

Explanation

When the train is approaching
`n_1=(v)/(v-v_s)xxn=(320)/(320-4)xx243=(80)/(79)xx243`
When the train is receding,
`n_2=(v)/(v+v_s)xxn=(320)/(324)xx243=(80)/(81)xx243`
Beat frequency is
`n=n_1-n_2=80xx243((1)/(79)-(1)/(81))=6Hz`