Question

Two sources P and Q produces notes of frequency $990\text{Hz}$ each. A listener moves from P to Q with a speed of $1{\text{ms}}^{-1}$. If the speed of sound is $330\text{m/s}$, then the number of beats heard by the listener per second is

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is C $6$


Apparent frequency due to P:
$f^{\prime }=\left(\frac{v-v_0}{v}\right)990=329\times 3\text{Hz}$
Apparent frequency due to Q:
$f^{\prime \prime }=\left(\frac{v+v_0}{v}\right)990=331\times 3\text{Hz}$
Beat frequency, $f_b=f^{\prime \prime }-f^{\prime }$
$f_b=3\times (331-329)=6\text{Hz}$