Question

A sound source emits frequency of $180\text{Hz}$ when moving towards a rigid wall with speed $5\text{m/s}$ and an observer is moving away from wall with speed $5\text{m/s}.$ Both source and observer moves on a straight line which is perpendicular to the wall. The number of beats per second heard by the observer will be $[\text{speed of sound}=355\text{m/s}]$

• A. $5\text{beats/s}$
• B. $10\text{beats/s}$
• C. $6\text{beats/s}$
• D. $8\text{beats/s}$

Answer 1

The correct option is D $8\text{beats/s}$

${\nu }_d=\frac{V+v_o}{V-v_s}{\nu }_s=\frac{355+5}{355-5}180=185.14\text{Hz}\approx 185\text{Hz}$,
${\nu }_r=\frac{V-v_o}{V}{\nu }_s=\frac{355-5}{355}180=177.46\text{Hz}\approx 177Hz$
${\nu }_d-{\nu }_r=185-177=8\text{beats/sec}$