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A car moving on a straight path with a s...

A car moving on a straight path with a speed of 54 km/h, passes by a stationary listener, playing hrn with a frequency 500 Hz. If velocity of sound in air is 340 m/s, find out the differenfce in frequencies of sound of horn, heard by stationary listener when car approaches him and recedes from him.

Text Solution

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Here `v_(S) = 54 (km )/(h) = 54 xx (5)/(18) (m)/(s) =15 (m)/(s)`
(i) When car approaches stationary listener,

We have, `(f_(L))/( v + v _(L)) = (f _(S))/(v + v _(S))`
`therefore ( f _(L))/( 340 + 0) = (500)/( 340 - 15)`
`therefore f _(L) = 500 xx (340)/(325) = 523.1 Hz.`
(ii) When car recedes away from stationary listener,

We have, `(f ._(L))/( v + v _L)= ( f _(S))/( v + v _(S))`
`therefore ( f ._(L))/( 340 + 0) = (500 )/(340+15)`
` therefore f ._(L) = 500 xx (340)/(355) = 478.9 Hz`
Required difference `=f _(L) -f._(L)`
`= 523.1-478.9`
`=44.2 Hz`
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