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).

A pipe 20 cm long is closed at one end, which harmonic mode of the pip

1.	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).
Answer» Solution :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)/40.2 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.