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A pipe 20cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 430Hz source? Will the same source be in resonance with the pipe if both ends are open? Take speed of sound in air `340m//s`. |
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Answer» Here, `L=20cm=0.2m, v_(n)=430Hz, upsilon=340ms^(-1)` The frequency of nth normal mode of vibration of closed pipe is `v_(n)=(2n-1)(upsilon)/(4L):. 430=(2n-1)(340)/(4xx0.2)` `2n-1=(430xx4xx0.2)/(340)=1.02` `2n=2.02, n=1.01` Hence it will be the 1st normal mode of vibration. In a pipe, open at both ends, we have `v_(n)=nxx(upsilon)/(2L)=(nxx340)/(2xx0.2)=430:. n=(430xx2xx0.2)/(340)=0.5` As n has to be an integer, therefore, open organ pipe cnnot be in resonance with the source . |
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