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`.

Explanation

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 .