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A pipe 20cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 430 Hz source ? Will the same source be in resonance with the pipe if both ends are open ? ( speed of sound in air is `340ms^(-1)`) |
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Answer» Here, `l= 20 cm=0.2m , v_(n) = 430 Hz,v= 340 m//s ` The frequency of `n^(th) ` normal mode of vibration of closed pipe s `v_(n) =( 2n-1) (v)/( 4l)` `:. 430 = ( 2n-1) ( 340)/( 4 xx 0.2)` `2n-1= ( 430 xx 4xx 0.2)/( 340)= 1.02 ` `2n =2.02 , n = 1.01 ` Hence it will be the`1^(st)` normal mode of vibration . In a pipe, open at both ends we have `v_(n) =n xx( v)/( 2l) = ( n xx 340 )/( 2 xx 0.2) = 430` ` :. n = ( 430 xx 2 xx 0.2)/( 340 ) =0.5 ` As n has to be an integer, therefore open organ pipe cannot be in resonance with the source. |
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