The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is [2023]

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Solution

Q.
The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is [2023]

1 1 : 3

2 3 : 1

3 1 : 2

4 2 : 1

Ans.
(4)

Fundamental frequency for open organ pipe,

$f_{o} = \frac{v}{2 L_{o}}$ ...(i)

Fundamental frequency for closed organ pipe,

$f_{c} = \frac{v}{4 L_{c}}$ ...(ii)

$\frac{f_{o}}{f_{c}} = \frac{v}{2 L_{o}} \times \frac{4 L_{c}}{v} \Rightarrow \frac{f_{o}}{f_{c}} = \frac{2}{1}$ $(∵ L_{o} = L_{c} (given))$

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