Sound WavesHardBloom L3
Question
As shown below there are 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 ω1 and ω2 respectively. If frequency of source is f then, frequency observed by observer is
(Given: ω1 = 10 rad/sec, ω2 = 10 rad/s, R = 10 m and velocity of sound is 330 m/s)
Options
A.$\frac{23}{43}f$
B.$\frac{47}{23}f$
C.$\frac{43}{23}f$
D.f
Solution
Sol. 
At the instant, shown velocity of source is along the line joining the source and observer
fobserved = $\left( \frac{v + 2R\omega_{2}\cos 60{^\circ}}{v - \omega_{1}R} \right)f$
= $\left( \frac{330 + 2 \times 10 \times 10 \times \frac{1}{2}}{330 - 10 \times 10} \right)f$
= $\frac{43}{23}f$
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