A person with a vibrating tuning fork of freq | vedclass

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(B) The person is moving towards a wall with a tuning fork. The frequency of the sound heard directly from the fork is $f = 338 \,Hz$.The frequency of

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$4$

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(B) The person is moving towards a wall with a tuning fork. The frequency of the sound heard directly from the fork is $f = 338 \,Hz$.The frequency of the sound reflected from the wall, $f'$, is perceived by the moving observer. Since the observer is moving towards the wall, the reflected sound acts as a source at rest and the observer is moving towards it.The formula for the frequency of the reflected sound heard by the observer is $f' = f \left( \frac{v + v_0}{v - v_s} ight)$.Here, the source (the wall reflecting the sound) is at rest, so $v_s = 0$. The observer is moving towards the wall with $v_0 = 2 \,ms^{-1}$.Thus, $f' = f \left( \frac{v + v_0}{v} ight) = 338 \left( \frac{340 + 2}{340} ight) = 338 \left( \frac{342}{340} ight) = 338 	imes 1.00588 \approx 340 \,Hz$.The beat frequency is the difference between the reflected frequency and the original frequency: $\Delta f = f' - f = 340 - 338 = 2 \,Hz$.Wait, let's re-evaluate: The observer is moving towards the wall. The sound reaches the wall and reflects back. The frequency of the reflected sound as heard by the observer is $f' = f \left( \frac{v + v_0}{v - v_0} ight)$ is incorrect because the source is the wall. The correct approach is: The wall receives sound of frequency $f_{wall} = f \left( \frac{v}{v - v_0} ight)$. The wall reflects this frequency, and the observer moving towards the wall receives $f' = f_{wall} \left( \frac{v + v_0}{v} ight) = f \left( \frac{v + v_0}{v - v_0} ight)$.Calculating: $f' = 338 \left( \frac{340 + 2}{340 - 2} ight) = 338 \left( \frac{342}{338} ight) = 342 \,Hz$.Beat frequency = $f' - f = 342 - 338 = 4 \,Hz$.

$A$ person with a vibrating tuning fork of frequency $338 \,Hz$ is moving towards a vertical wall with a speed of $2 \,ms^{-1}$. The velocity of sound in air is $340 \,ms^{-1}$. The number of beats heard by that person per second is

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