Two tuning forks $A$ and $B$ lying on opposite sides of observer $^{'} O^{'}$ and of natural frequency $85 H z$ move with velocity $10 m / s$ relative to stationary observer $O$ . Fork $A$ moves away from the observer while the fork $B$ moves towards him. A wind with a speed $10 m / s$ is blowing in the direction of motion of fork $A$ . Find the beat frequency measured by the observer in $H z$ . [Take speed of sound in air as $340 m / s$ ]

5

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Solution

The correct option is C $7$
$\begin{matrix} f o r A : f_{A} = (\frac{C + 10 + 0}{C + 10 + 10}) f o = \frac{340}{360} f o = \frac{34}{36} f o f o B : f_{B} = (\frac{C + 10}{C + 10 - 10}) f o = \frac{350}{340} f o = \frac{35}{34} f o Δ f = f_{B} - f_{A} = [\frac{35}{34} - \frac{34}{36}] f o \approx 7 ∴ b e t a f r e q u e n c y \approx 7 \end{matrix}$
Hence,
option $C$ is correct answer.

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The correct option is C 7forA:fA=(C+10+0C+10+10)fo=340360fo=3436fofoB:fB=(C+10C+10−10)fo=350340fo=3534foΔf=fB−fA=[3534−3436]fo≈7∴betafrequency≈7Hence,option C is correct answer.