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  • 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 the same source be in resonance with the pipe if both ends are open?

Q.15.17  A pipe 20\: cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a source? Will the same source be in resonance with the pipe if both ends are open? (speed of  sound in air is 340\:m\: s^{-1}).

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Let the nth harmonic mode of the pipe get resonantly excited by a 430 Hz source.

\\\frac{(2n-1)v}{4l}=\nu \\ 2n-1=\frac{430 \times 4\times 0.2}{340}\\ n=1

The pipe resonates with a 430 Hz source in the fundamental mode when one end is open.

Let the mth harmonic mode of the pipe get resonantly excited by a 430 Hz source when both ends are open.

\\\lambda =\frac{2l}{m}\\ m=\frac{2l\nu }{v}\\ m=\frac{2\times 0.2\times 430}{340}\\ m=0.5

Since m is coming out to be less than 1 the same source will not be in resonance with the pipe if both ends are open.

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Sayak

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