Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed 1.0 and the man behind walks at a speed 2.0 . A third man is standing at a height 12 m above the same horizontal line such that all three men ar

Question

Two men are walking along a horizontal straight line in the same direction. The man in front walks at a speed 1.0 ${ms}^{- 1}$ and the man behind walks at a speed 2.0 ${ms}^{- 1}$ . A third man is standing at a height 12 m 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 1430 Hz. The speed of sound in air is 330 ${ms}^{- 1}$ . At the instant, when the moving men are 10 m apart, the stationary man is equidistant from them. The frequency of beats in Hz, heard by the stationary man at this instant, is ____________. [2018]

Smart Achievers · Accepted Answer

(5)

$Apparent frequency at O due to source at - A$

$ν_{A} = ν [\frac{v}{v - 2 \cos θ}]$

$Apparent frequency at O due to source at - B$

$ν_{B} = ν [\frac{v}{v + \cos θ}]$

$∴$ $Beat frequency, ν_{b} = ν [\frac{v}{v - 2 \cos θ}] - ν [\frac{v}{v + \cos θ}]$

$= ν v [\frac{1}{v - 2 \cos θ} - \frac{1}{v + \cos θ}]$

$= 1430 \times 330 [\frac{1}{330 - 2 \times \frac{5}{13}} - \frac{1}{330 + \frac{5}{13}}]$

$= 1430 \times 330 \times 13 [\frac{1}{330 \times 13 - 10} - \frac{1}{330 \times 13 + 5}]$

$= 1430 \times 330 \times 13 [\frac{1}{4280} - \frac{1}{4295}] \approx 5 Hz$

Solution

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