Question

Two person A and B, each carrying a source of frequency 300 Hz, are standing a few metre apart. A starts moving towards B with velocity 30 m/s. If the speed of sound is 300 m/s, which of the following is true ?

• A. number of beats by A is higher than that heard by B
• B. the number of beats by B are 30 Hz
• C. both (a) and (b) are correct
• D. both (a) and (b) are wrong

Answer 1

Answer: (D)

both (a) and (b) are wrong

Speed of sound $v_{sound}=300m/s$
Frequency of source $f=300Hz$
Velocity of A $v_A=30m/s$
Let apparent frequencies heard by $B$ and $A$ be $f^{\prime }$ and $f^{\prime \prime }$ respectively.
Doppler effect when source $\left(A\right)$ moves towards the stationary observer $\left(B\right)$:
Apparent frequency heard by B $f^{\prime }=f[\frac{v_{sound}}{v_{sound}-v_{source}}]=300[\frac{300}{300-30}]=333.3Hz$
Thus beat frequency by $B$ $b_B=f^{\prime }-f=333.3-300=33.3Hz$
Doppler effect when observer $\left(A\right)$ moves towards the stationary source $\left(B\right)$:
Apparent frequency heard by A $f^{\prime \prime }=f[\frac{v_{sound}+V_{observer}}{v_{sound}}]=300[\frac{300+30}{300}]=330Hz$
Thus beat frequency by $A$ $b_A=f^{\prime }-f=330-300=30Hz$
Hence both (a) and (b) are wrong.