An open pipe is suddenly closed with the result that the second overtone of the closed pipe is observed to be higher in frequency by 100 - than the fundamental frequency of the original pipe- The fundamental frequency of the open pipe will be

Name: CENGA - Grade 11 - Physics - Sounds - Q63
Uploaded: 2022-07-04T10:36:42+05:30
Description: The frequency of m^th harmonic in an open organ pipe, ⇒ v_m = mv2l Fundamnetal frequency for open organ pipe, m =1 nbsp; nbsp; nbsp;⇒ v_1 = v2l The f ...

The frequency of m^th harmonic in an open organ pipe, ⇒ v_m = mv2l Fundamnetal frequency for open organ pipe, m =1 nbsp; nbsp; nbsp;⇒ v_1 = v2l The f ...

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Standard IX

Physics

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An open pipe ...

Question

An open pipe is suddenly closed with the result that the second overtone of the closed pipe is observed to be higher in frequency by $100 H z$ than the fundamental frequency of the original pipe. The fundamental frequency of the open pipe will be

300 H z

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100 H z

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150 H z

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200 H z

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Solution

The correct option is D $200 H z$
The frequency of $m^{t h}$ harmonic in an open organ pipe,
$\Rightarrow v_{m} = \frac{m v}{2 l}$

Fundamnetal frequency for open organ pipe, $m = 1$
$\Rightarrow v_{1} = \frac{v}{2 l}$

The frequency of $n^{t h}$ harmonic in a closed organ pipe,
$\Rightarrow v_{n} = \frac{n v}{4 l}$

The second overtone of the closed pipe is observed to be higher in frequency by $100 H z$ than the fundamental of the original pipe.
$\Rightarrow \frac{3 v}{4 l} - \frac{v}{2 l} = 100 H z$
$\Rightarrow \frac{v}{l} = 400 H z$

Fundamental frequency for open organ pipe,
$\Rightarrow v_{1} = \frac{v}{2 l}$
$\Rightarrow v_{1} = \frac{400 H z}{2}$
$\Rightarrow v_{1} = 200 H z$

Final Answer : (d)

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An open pipe is suddenly closed with the result that the second overtone of the closed pipe is observed to be higher in frequency by 100 Hz than the fundamental frequency of the original pipe. The fundamental frequency of the open pipe will be

An open pipe is suddenly closed with the result that the second overtone of the closed pipe is observed to be higher in frequency by $100 H z$ than the fundamental frequency of the original pipe. The fundamental frequency of the open pipe will be