A source of sound $S$ is moving with the velocity of $50\,m/s$ towards a stationary observer. The observer measures the frequency of the sound as $1000\,Hz.$ What will be the apparent frequency of the source when it is moving away from the observer after crossing him ... $Hz$ ? (Take velocity of sound in air is $350\,m/s$ )
JEE MAIN 2019, Medium
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$\mathrm{f}_{\mathrm{a}}=\frac{\mathrm{V}}{\mathrm{V}-\mathrm{V}_{\mathrm{s}}} \mathrm{f}_{\mathrm{o}}=1000 \mathrm{Hz}$
$\mathrm{f}_{\mathrm{a}}^{\prime}=\frac{\mathrm{V}}{\mathrm{V}+\mathrm{V}_{\mathrm{s}}} \mathrm{f}_{\mathrm{o}}$
$\frac{f_{a}^{\prime}}{f_{a}}=\frac{V-V_{s}}{V+V_{s}}=\frac{350-50}{350+50}=\frac{300}{400}=\frac{3}{4}$
$\mathrm{f}_{\mathrm{a}}^{\prime}=\frac{3}{4} \times 1000=750 \mathrm{Hz}$
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