Question

A person with vibrating tuning fork of frequency $338$Hz is moving towards a vertical wall with a speed of $2m{s}^{-1}$. Velocity of sound in air is $340m{s}^{-1}$. The number of beats heard by that person per second is.

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (B)

$4$

Velocity of sound $v=340m/s$

Velocity of source $v_s=2m/s$

Original frequency of tuning fork ${\nu }_o=338$ Hz

Apparent frequency heard by any man on wall (Doppler effect when a source moves towards stationary observer) :

${\nu }^{\prime }={\nu }_o[\frac{v}{v-v_s}]=\left(338\right)\times \frac{340}{340-2}=340$ Hz

Apparent frequency heard by the person, coming after reflection from wall (Doppler effect when an observer moves towards stationary source) :

${\nu }^{\prime \prime }={\nu }^{\prime }[\frac{v+v_o}{v}]=\left(340\right)\times \frac{340+2}{340}=342$ Hz

Thus number of beats heard by person $b={\nu }^{\prime \prime }-{\nu }^{\prime }$

$\therefore$ $b=342-338=4$ per second