A train approaching a railway crossing at a speed of 120 km/h sounds a whistle of frequency 576 Hz, when it is 288 m away from the crossing . The frequency heard by the observer standing on the road perpendicular to the track from the crossing at a distance of 384 m is
(Speed of sound in air ` = 340 ms^(-1)` )

Options

A. 632 Hz
B. 612 Hz
C. 512 Hz
D. 472 Hz

Answer

B

Explanation

According to the questionn.
When a sound source is moving towards a stationary observer with speed u and the speed of sound is v, then frequaency heard by observer,
` f. = ((v)/(v - u))f`
Given, frequency of whistle sound , f = 567 Hz
speed of sound , v = 340 m/s speed of train u = 120 km/ hr
speed of observer,
` = 120 xx (5)/(18 cos theta = 120 xx (5)/(18) xx ((228)/(sqrt((384)^(2)+(288)^(2))))`
`u= 120 xx(5)/(18) xx (3)/(5) = 20 m//s`
Hence, frequency heard by observer,
`f. = ((340)/(340 - 20)) xx 576`
`- 612 Hz`