Question

$A$ and $B$ are two sources generating sound waves. A listener is situated at $C$. The frequency of the source at $A$ is $500Hz$. A, now, moves towards $C$ with a speed $4m/s$. The number of beats heard at $C$ is $6$. When $A$ moves away from $C$ with speed $4m/s$, the number of beats heard at $C$ is $18$. The speed of sound is $340m/s$. The frequency of the source at $B$ is :

• A. $500Hz$
• B. $506Hz$
• C. $512Hz$
• D. $5494Hz$

Answer 1

Answer: (C)

$f=500Hz$
Case 1 : When source is moving towards stationary listener
apparent frequency ${\eta }^{\prime }=\eta \left(\frac{v}{v-v_s}\right)$
$=500\left(\frac{340}{336}\right)=506Hz$
Case 2 : When source is moving away from the stationary listener
${\eta }^{\prime \prime }=\eta \left(\frac{v}{v+v_s}\right)=500\left(\frac{340}{344}\right)=494Hz$
In case 1 number of beats heard is 6 and in case 2 number ofbeats heard is 18 therefore frequency of the source at $B=512Hz$