A source of sound S emitting waves of frequen | vedclass

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(A) Given:Frequency of source,$f_{0} = 100 \, Hz$Velocity of source,$v_{s} = 19.4 \, m s^{-1}$Velocity of sound in air,$v = 330 \, m s^{-1}$The compon

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$97$

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(A) Given:Frequency of source,$f_{0} = 100 \, Hz$Velocity of source,$v_{s} = 19.4 \, m s^{-1}$Velocity of sound in air,$v = 330 \, m s^{-1}$The component of the source velocity along the line joining the source and the observer is $v_{s} \cos 60^{\circ}$. Since the source is moving away from the observer,the apparent frequency $f'$ is given by the Doppler effect formula:$f' = f_{0} \left( \frac{v}{v + v_{s} \cos 60^{\circ}} ight)$Substituting the values:$f' = 100 \left( \frac{330}{330 + 19.4 	imes \cos 60^{\circ}} ight)$$f' = 100 \left( \frac{330}{330 + 19.4 	imes 0.5} ight)$$f' = 100 \left( \frac{330}{330 + 9.7} ight)$$f' = 100 \left( \frac{330}{339.7} ight) \approx 97.14 \, Hz$Rounding to the nearest integer,the apparent frequency is $97 \, Hz$.

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