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JEE Advanced 2018Paper 1
Exam
JEE Advanced
Year
2018
Paper
Paper 1
Subject
Physics
Chapter
Waves and Sound

JEE Advanced 2018 · Paper 1 · Physics · Waves and Sound

Two men are walking along a horizontal straight line in the same...

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed 1.0ms−11.0m{s}^{- 1} and the man behind walks at a speed 2.0ms−12.0m{s}^{- 1} . A third man is standing at a height 12m12m above the same horizontal line such that all three men are in a vertical plane. The two walking men are blowing identical whistles which emit a sound of frequency 1430Hz1430Hz . The speed of sound in air is 330ms−1.330m{s}^{- 1} . At the instant, when the moving men are 10m10m apart, the stationary man is equidistant from them. The frequency of beats in HzHz , heard by the stationary man at this instant, is __________.Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed 1.0m s ^

Correct answer

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Step-by-step solution

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed 1.0m s ^ 
cosθ=513cos \theta = \dfrac{5}{13}
fA=1430{f}_{A} = 1430\left[\dfrac{330}{330 - 2cos \theta}\right] = 1430\left[\dfrac{1}{1 - \dfrac{2cos \theta}{330}}\right] = 1430\left[1 + \dfrac{2cos \theta}{330}\right](Bybinomialexpansion)<br>(By binomial expansion)<br >{f}_{B} = 1430\left[\dfrac{330}{330 + 1cos \theta}\right] = 1430\left[1 - \dfrac{cos \theta}{330}\right]<br><br >∆ f = {f}_{A} - {f}_{B} = 1430\left[\dfrac{3cos \theta}{330}\right] = 13cos \theta<br><br >= 13\left(\dfrac{5}{13}\right) = 5.00Hz
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