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

l = 20 cm = 0.20 m
For fundamental note,
`v_(1) = (upsilon)/(lambda_(1)) = (upsilon)/(4l)`
`v_(1) = (upsilon)/(4l) = (upsilon)/(4 xx 2) = (340 xx 10)/(8)`
= 425 Hz
Hence first harmonic or fundamental note of the pipe can be excited by a 430 Hz source when the pipe is closed at one end.
When both ends of pipe are open then the fundamental frequency of vibration of open organ pipe
`= (upsilon)/(2l)` = 850 Hz
Hence the same source of frequency will not be in resonance with the open organ pipe.