30.Two tuning forks with natural fequencies340HZ each move relative to a stationary observer.One fork moves away from the listener.while the other moves towards him at the same speed.The listener hears beats of frequency 3HZFind the speed of the fork (velocity of sound in air =340m/s).--------

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Solution

$a p p a r e n m t f r e q u e n c y i s g i v e n b y : f = (\frac{v}{v + v_{s}}) f_{0} f_{0} i s t h e i n i t a l f r e q u e n c y = 340 H z v = 340 m / s w h e n f o r k m o v e s t o w a r d s t h e l i s t e n e r f_{1} = (\frac{v}{v + v_{s}}) f_{0} w h e n f o r k m o v e s a w a y f r o m t h e l i s t n e r f_{2} = (\frac{v}{v - v_{s}}) f_{0} b e a t f r e q u e n c y i s n g i v e n b y " : f = f_{2} - f_{1} = (\frac{v}{v - v_{s}}) f_{0} - (\frac{v}{v + v_{s}}) f_{0} 3 = \frac{2 v v_{s} f_{0}}{v^{2} - {v_{s}}^{2}} \frac{v^{2} - {v_{s}}^{2}}{v_{s}} = \frac{2 v f_{0}}{3} o n s o l v i o n g t h e a b o v e e q u a t i o n y o u c a n f i n d t h e v a l u e o f v_{s}$

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