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  • A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of 30 m/s.If both trains emit sounds with frequency 300 Hz, (Speed of

A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of 30 m/s.If both trains emit sounds with frequency 300 Hz, (Speed of sound: \frac{300m}{s}) approximate difference of frequencies heard by the person will be:
 

Option: 1

55 Hz 


Option: 2

80 Hz 


Option: 3

33 Hz 


Option: 4

10 Hz


Answers (1)

best_answer

\begin{aligned} & \mathrm{f}_0=300 \mathrm{~Hz} \\ & \mathrm{~V}=330 \mathrm{~m} / \mathrm{sec} . \\ & \mathrm{f}_{\mathrm{A}}=\mathrm{f}_0\left[\frac{\mathrm{V}}{\mathrm{V}-\mathrm{V}_{\mathrm{A}}}\right]=300\left[\frac{330}{330-30}\right]=330 \mathrm{~Hz} \\ & \mathrm{f}_{\mathrm{B}}=\mathrm{f}_0\left[\frac{\mathrm{V}}{\mathrm{V}+\mathrm{V}_{\mathrm{A}}}\right]=300\left[\frac{330}{360}\right]=275 \mathrm{~Hz} \\ & \Delta \mathrm{f}=\mathrm{f}_{\mathrm{A}}-\mathrm{f}_{\mathrm{B}}=330-275=55 \mathrm{~Hz} \end{aligned}

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