The frequency of the whlstle of a train Is 512 Hz . The train crosses a station at a speed of 72 km . `h^(-1)` Calculate the frequency of the sound heard by a Iistener, standing on the platform , before and after the train crosses the station. Neglect the effect of wind . Velocity of sound is 336 , m `s^(-1)` .

Explanation

Velocity of the train ` = 72 km . `h^(-1)`
` = (72 xx1000)/(60xx60) m. s^(-1)`
`= 20 m. s^(-1)`
When the train approaches the station , the distance covered hy 512 sound waves = 336 - 20 = 316` m
` therefore ` Apparent wavelength , ` lambda . = (316)/(512) m `
` therefore ` Apparent frequency due to Doppler effect
` = (" velocity of sound (V))/(lambda .)`
`(336)/((316)/(512)) = (336xx512)/(316) = 544.4 Hz `
` Again , when the train recedes from the station , the distance covered y 512 sound waves = 366 + 20 = 356 m
` therefore ` Apparent wavelength , ` lambda . = (356)/(512) m`
` therefore ` Apparent freaquency = `(V) /(lambda .) = (336)/((356)/(512)) = (336xx 512)/(356) = 483.2 Hz .`