A motorcyclist is approaching a large wall with a velocity of $90\,km/hr$. A car is chasing him with a velocity of $108\,km/hr$. If the car sounds a horn at $30\,Hz,$ beat frequency heard by motorcyclist is ____ $Hz$ . Take velocity of sound $= 330\,m/s$ .
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$\mathrm{v}_{\mathrm{S}}=30, \mathrm{f}_{\mathrm{s}}=30, \mathrm{v}_{0}=25, \mathrm{v}=330$
$\mathrm{f}_{1}=\mathrm{f}_{\mathrm{s}}\left(\frac{\mathrm{v}-\mathrm{v}_{0}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right)$
$\mathrm{f}_{2}=\mathrm{f}_{\mathrm{s}}\left(\frac{\mathrm{v}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right)\left(\frac{\mathrm{v}+\mathrm{v}_{0}}{\mathrm{v}}\right)=\mathrm{f}_{\mathrm{s}}\left(\frac{\mathrm{v}+\mathrm{v}_{0}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right)$
$\mathrm{f}_{\text {beat }}=\frac{2 \mathrm{f}_{\mathrm{s}} \mathrm{v}_{0}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}=\frac{2 \times 30 \times 25}{300}=5$
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