Question

A pipe 30.0 cm long is open at both ends. Which harmonic mode of the pipe resonates with a 1.1kHz source? Will resonance with the same source be observed if one end of the pipe is closed ? Take the speed of sound in air as `330ms^(-1)`.

Answer 1

Here, `L=30.0cm=0.3m`
Let, nth harmonic of open pipe resonate with 1.1kHz source, i.e., `v_(n)=1.1kHz=110Hz`
As, `v_(n) =(n upsilon)/(2L)`
`:. n=(2Lv_(n))/(upsilon)=(2xx0.30xx1100)/(330)=2`
i.e., 2nd harmonic resonates with open pipe.
If one end of pipe is closed, its fundamental frequency `v_(1)=(upsilon)/(4L)=(330)/(4xx0.3)=275Hz.` As odd harmonics alone are produced in a closed organ pipe, therefore, possible freqencies are `3v_(1)=3xx275=825Hz, 5v_(1)=5xx275=1375Hz` and so on. As the source freqency is 1100 Hz, therefore, no resonance can occur when the pipe is closed at one end.