A railway track and road are in mutually perpendicular . A train is approaching the railway crossing with a speed 80 km/h.
When the train is at a distance 1 km from the crossing it blows whistle of frequency 400 Hz
which frequency of sound will be heard by a man on a road at a distance 600 m from the crossing ? volecity of sound = 330 m ` s^(-1) ` .

Explanation

Train (S) is moving with velocity 80 km/h along SA. At a time of blowing whistle , distances of train and a man (O) from the crossing (A) are 1 km and 600 m respectively .
` (##CHY_DMB_PHY_XI_P2_U10_C05_SLV_009_S01.png" width="80%">
` therefore SA = 1 km = 1000 m , OA = 600 m `
If ` u_(S) ` be the velocity of the train , component along SO is ` u_(2) cos theta ` .
` therefore cos theta = (SA) /(SO) = (SA)/(sqrt(SA^(2) + AO^(2))) = (100) /(sqrt(((1000)^(2) + (600)^(2))) = 0.8575 `
` therefore u_(S) cos theta = 80 xx (5)/(18) xx 0.8575 = 19.05 m * s^(-1)`
` therefore ` Apparent frequency of sound , n. ` = (V)/(V - u_(S) cos theta )n `
Here , V = velocity of sound `= 330 m * s^(-1)`
and actual frequency , n = 400 Hz
` therefore n. = (330)/(330 - -19.05) xx 400 424.5 Hz ` .