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A train approaching a railway crossing at a speed of 120 km/hr sounds a short whistle at frequency $f_{o} = 640 H z .$ When it is 300 m away from the crossing. The speed of sound in air is 340 m/sec. A person standing on a road perpendicular to the track at a distance 400 m from the crossing , hears frequency $f_{1} .$ The value of $f_{1} - f_{0} = 10 x .$ Find the value of x

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Detailed Solution

A train approaching a railway crossing at a speed of 120 km/h sounds a short whistle at frequency 640 Hz when it is 300 m away from the crossing. - Sarthaks eConnect |

The component of the velocity of train along the line joining to the person is $v_{s} cosθ$

here, $v_{s} = \frac{100}{3} {ms}^{- 1}$ , $cosθ = \frac{3}{5}$

$f_{ap} = f_{0} [\frac{v + v_{o}}{v - v_{s} cosθ}] = 640 (\frac{340}{340 - \frac{3}{5} \times \frac{100}{3}}) = 680 Hz$

So, $f_{1} - f_{0} = 40 Hz$

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