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(B) The sound from the source $P$ reaches the observer at $Q$ along the path $PQ$. The source $P$ is approaching the crossing with a velocity $v_{s} =

Vedclass · Accepted Answer

$717$

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(B) The sound from the source $P$ reaches the observer at $Q$ along the path $PQ$. The source $P$ is approaching the crossing with a velocity $v_{s} = 10\, m/s$.When the observer in car $Q$ hears the sound of the horn,the effective velocity of approach of the car $P$ towards the observer is $v_{s} \cos 	heta$.From the geometry of the problem,the distance $PQ = \sqrt{40^2 + 30^2} = 50\, m$. Thus,$\cos 	heta = \frac{40}{50} = \frac{4}{5}$.The apparent frequency $f'$ heard by the observer is given by the Doppler effect formula:$f' = \left( \frac{v}{v - v_{s} \cos 	heta} ight) f$Substituting the given values:$f' = \left( \frac{340}{340 - 10 	imes \frac{4}{5}} ight) 	imes 700$$f' = \left( \frac{340}{340 - 8} ight) 	imes 700 = \frac{340}{332} 	imes 700$$f' \approx 1.024 	imes 700 \approx 716.86\, Hz$Rounding to the nearest integer,we get $f' \approx 717\, Hz$.

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