Question

A source of sound 'S' emitting waves of frequency $100Hz$ and an observer 'O' are located at some distance from each other. The source is moving with a speed of $19.4m{s}^{-1}$ at an angle of ${60}^o$ with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer is
(velocity of sound in air $330m{s}^{-1}$)

• A. $97Hz$
• B. $100Hz$
• C. $103Hz$
• D. $106Hz$

Answer 1

The correct option is C $103Hz$

Since the source has a component of velocity along 'SO', the apparent frequency observed by the observer will increase.
$v$: velocity of sound
Velocity of observer is zero
Velocity of the source along 'SO' $v_s=19.4\times \cos \left({60}^0\right)=9.7m/s$
$f_0=$ frequency emitted by source
$f_{apparent}=f_0\left(\frac{v-v_o}{v-v_s}\right)$$=100\times \left(\frac{330-0}{330-9.7}\right)=103.03Hz$