An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

200 Hz

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300 Hz

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240 Hz

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480 Hz

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Solution

The correct option is A 200 Hz
$∴$ Frequency $= \frac{v}{λ_{1}} = \frac{v}{2 l} ∴ v_{1} = \frac{v}{2 l} . . . (i)$
For closed pipe, vibrating in third harmonic, Frequency = $\frac{3 v}{4 l}$
or $v_{2} = \frac{3 v}{4 l}$
$v_{2} - v_{1} = 100$ (given)
$∴ \frac{3 v}{4 l} - \frac{v}{2 l} = 100 o r \frac{v}{4 l} = 100 o r v = 400 l$
$∴ v_{1} = \frac{v}{2 l} = \frac{400 l}{2 l} = 200 H z$
$∴$ Fundamental frequency of open pipe = 200 Hz

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Q. An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

Q. An open pipe is suddenly closed one end with the result that the frequency of the third harmonic of the closed pipe is found to be higher by

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Q. An open pipe is suddenly closed at one end as a result of which the frequency of the third harmonic of the closed pipe is found to be higher by

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than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

An open pipe is suddenly closed at one end and with the result frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. What is the fundamental frequency of the open pipe?

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An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

The correct option is A 200 Hz ∴ Frequency =vλ1=v2l ∴v1=v2l ...(i) For closed pipe, vibrating in third harmonic, Frequency = 3v4l or v2=3v4l v2−v1=100 (given) ∴3v4l−v2l=100 or v4l=100 or v=400 l ∴v1=v2l=400l2l=200Hz ∴ Fundamental frequency of open pipe = 200 Hz