A source S emitting sound of frequency 288 ,H | vedclass

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Question

(C) The frequency observed is maximum when both the observer $O$ and the source $S$ are moving towards each other with their maximum speeds.
For simp

Vedclass · Accepted Answer

$324$

Vedclass · Answer

(C) The frequency observed is maximum when both the observer $O$ and the source $S$ are moving towards each other with their maximum speeds.
For simple harmonic motion, the maximum speed is given by $v_m = A\omega$, where $A$ is the amplitude and $\omega$ is the angular velocity.
Given $A = 0.5 \,m$ and $\omega = 40 \,rad/s$, the maximum speed of each block is:
$v_m = 0.5 	imes 40 = 20 \,m/s$.
According to the Doppler effect, the observed frequency $f'$ is given by:
$f' = f \left( \frac{v + v_o}{v - v_s} ight)$
where $v = 340 \,m/s$ is the speed of sound, $v_o = 20 \,m/s$ is the speed of the observer moving towards the source, and $v_s = 20 \,m/s$ is the speed of the source moving towards the observer.
Substituting the values:
$f_{\max} = 288 	imes \left( \frac{340 + 20}{340 - 20} ight)$
$f_{\max} = 288 	imes \left( \frac{360}{320} ight)$
$f_{\max} = 288 	imes 1.125 = 324 \,Hz$.

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