Question

As shown above there is two circles having radius $R$ and $2R$ respectively. Sound source is moving in inner circle in anticlockwise direction. Observer is moving on outer circle in clockwise direction with angular velocity ${\omega }_{1}and{\omega }_2$ respectively. If frequency of source is $f$ then, frequency observed by observer is :
(Given: ${\omega }_1=10rad/sec,{\omega }_2=10rad/s,R=10m$ and velocity of sound is $330m/s$)

• A. $\frac{23}{43}f$
• B. $\frac{47}{23}f$
• C. $\frac{43}{23}f$
• D. $f$

Answer 1

The correct option is C $\frac{43}{23}f$

The apparent frequency, $f^{{}^{\prime }}=\left(\frac{V+V_0}{V-V_s}\right)f$
$V_0={\omega }_2\times 2R\cos 60°=10\times 20\times \frac{1}{2}=100㎧$
$V_s={\omega }_1\times R=10\times 10=100㎧$
$V=330㎧$
$\therefore f^1=\left(\frac{330+100}{330-100}\right)f$
$\Rightarrow f^{{}^{\prime }}=\frac{430}{230}f$
$\therefore f^{{}^{\prime }}=\frac{43}{23}f$