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Two tuning forks are vibrating with natu...

Two tuning forks are vibrating with natural frequency of 510 Hz . One tuning fork moves away from the stationary observer, while the other moves towards him at the same speed. The observer hears beats of frequency 6 Hz. The speed of each tuning fork is -- m/s. (speed of sound in air = 340m/s)

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The correct Answer is:
2
`f _(1) - f _(2) = 6 hz`
`implies f ((v)/( v - v_(s)) ) - f ((v)/( v + v _(s))) = 6`
`implies 510 (( 340)/( 340 - v _(s))) - 51 (( 340)/( 340 + v _(t))) = 6`
`implies 510 [ (1- (v _(s))/( 340))^(-1) - (1 + (v _(s))/( 340)) ^(-1) ]=6`
As `v _(s) lt lt 340 m//s`
Using binomial approximation,
`implies 510 [ 1 + (v _(s))/( 340) - 1 + (v _(s))/ (340) ] = 6`
`implies ( 510 xx 2 v _(1))/( 340) = 6`
`implies v _(s) = ( 340 xx 6)/( 2 xx 510) = 2 m //s`
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Knowledge Check

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