A pipe 20 cm long is closed at one end, which harmonic mode of the pipe is resonantly excited by a 430 Hz source? Will this same source can be in resonance with the pipe, if both ends are open? Speed of sound = `340ms^(-1)`.

Explanation

The frequency of `n^(th)`mode of vibtration of a pipe closed at one end is given by
`v_(n)=((2n-1)v)/(4L)` river `v=340ms^(-1),L=20cm =0.2m,v^(n)=430Hz`
`therefore 430=((2n-1)**340)/4**0.2 Rightarrow n=1`. Therefore, first mode of vibration of the pipe is excited, for open pipe since n must be an integer, the same source cannot be in resonance with the pipe with both ends open.