The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If the length of the open pipe is 60 cm, the length of the closed pipe will be

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Solution

Q.
The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If the length of the open pipe is 60 cm, the length of the closed pipe will be [2024]

1 30 cm

2 45 cm

3 60 cm

4 15 cm

Ans.
(4)

$\frac{λ}{4} = L_{1}$ $2 (\frac{λ}{2}) = λ = L_{2}$

$f_{1} = \frac{v}{4 L_{1}}$ $f_{2} = \frac{v}{L_{2}}$

$f_{1} = f_{2}$

$\frac{v}{4 L_{1}} = \frac{v}{L_{2}} \Rightarrow L_{2} = 4 L_{1}$

$60 = 4 \times L_{1} \Rightarrow L_{1} = 15 cm$

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