A locomotive approaching a crossing at a spee | vedclass

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Question

(C) The observer is at point $O$ and the locomotive is at point $S$. The crossing is at point $C$. The distance $SC = 1 \, km$ and $OC = \sqrt{3} \, k

Vedclass · Accepted Answer

$660$

Vedclass · Answer

(C) The observer is at point $O$ and the locomotive is at point $S$. The crossing is at point $C$. The distance $SC = 1 \, km$ and $OC = \sqrt{3} \, km$.In the right-angled triangle $SCO$,the angle $	heta$ at $S$ is given by $	an 	heta = \frac{OC}{SC} = \frac{\sqrt{3}}{1} = \sqrt{3}$.Therefore,$	heta = 60^{\circ}$.According to the Doppler effect for a moving source and a stationary observer,the apparent frequency $f'$ is given by:$f' = f \left( \frac{c}{c - v \cos 	heta} ight)$where $c = 330 \, m/s$ is the speed of sound,$v = 20 \, m/s$ is the speed of the source,and $f = 640 \, Hz$ is the source frequency.Substituting the values:$f' = 640 \left( \frac{330}{330 - 20 \cos 60^{\circ}} ight)$Since $\cos 60^{\circ} = 0.5$:$f' = 640 \left( \frac{330}{330 - 20 	imes 0.5} ight) = 640 \left( \frac{330}{330 - 10} ight) = 640 \left( \frac{330}{320} ight)$$f' = 640 	imes \frac{33}{32} = 20 	imes 33 = 660 \, Hz$.

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