First slide

Stationary waves

Question

A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. What is the ratio of lengths

Moderate

A

1 : 2
B

2 : 1
C

2 : 3
D

4 : 3

Solution

Let $l_{1}$ and $l_{2}$ be the length’s of closed and open pipes respectively. (Neglecting end correction)
$l_{1} = \frac{λ_{1}}{4} \Rightarrow λ_{1} = 4 l_{1}$ and $l_{2} = \frac{λ_{2}}{2} \Rightarrow λ_{2} = 2 l_{2}$
Given $n_{1} = n_{2}$ so $\frac{v}{λ_{1}} = \frac{v}{λ_{2}} \Rightarrow \frac{v}{4 l_{1}} = \frac{v}{2 l_{2}} = \frac{l_{1}}{l_{2}} = \frac{1}{2}$

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