The first overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe 3.6 m in length. What is the length of the open organ pipe? (4.8m) 



Given:

Length of the closed pipe = L₁ = 3.6 m

The first overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe i.e.

(f₁)open = (f₁)closed --------------(1)

To Find:

Length of the open pipe = L₂ = ?


Solution:

Since  


(f₁)open = `\frac {v}{2 L₂}`

and

(f₁)closed = `\frac {v}{4 L₁}`

So equation (1) is

(f₁)open = (f₁)closed

`\frac {v}{2 L₂}` = `\frac {v}{4 L₁}`

2 L₂ = 4 L₁

or

L₂ = 2 L₁ = 2 ｘ 3.6 m = 7.2 m ------------Ans



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