Question

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

• A. 10
• B. 6
• C. 4
• D. 1

Answer 1

The correct option is B 6

When the train is approaching,
$n_1=\frac{v}{v-v_s}\times n=\frac{320}{320-4}\times 243=\frac{80}{79}\times 243$
When the train is receding,
$n_2=\frac{v}{v+v_s}\times n=\frac{320}{324}\times 243=\frac{80}{81}\times 243$
Beat frequency is
$n=n_1-n_2=80\times 243(\frac{1}{79}-\frac{1}{81})=6Hz$