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Two tuning forks with natural frequencie...

Two tuning forks with natural frequencies `340 H_(Z)` each move relative to a stationary observer . One forks moves away from the oberver while the other moves towards him at the same speed . The observer hearts beats of frequency `3 H_(Z)` . Find the speed the of the tuning fork (velocity of sound in air is `340 m//s)` .

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The correct Answer is:
A, B, C, D
Given, `f_(1) - f_(2) = 3`
or `((nu)/(nu - nu_(s))) f - ((nu) / (nu +nu_(s))) f = 3`
or `[(1)/((nu - nu_(s) /(nu)))- (1) / ((1 +nu_(s) / (nu)))] f= 3`
or `[(1-nu_(s)/(nu))^(-1) -(1+nu_(s)/(nu))^(-1)] f= 3`
or `[(1+nu_(s)/(nu)) -(1-nu_(s)/(nu))] f= 3`
or `(2nu_(s)f)/ (nu) = 3`
or Speed of tuning fork, `nu_(s) = (3nu)/(2f)`
subsituting the values, we get
`nu_(S)= ((3)(340))/((2)(340))= 1.5 m//S`
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