First slide

Experiments to find speed of sound

Question

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm the length of the open organ pipe is

Moderate

A

13.2 cm
B

8 cm
C

12.5 cm
D

16 cm

Solution

$For closed organ pipe, third harmonic is \frac{3 v}{4 l}$
$For open organ pipe, fundamental frequency is \frac{v}{2 l^{'}}$
Given, third harmonic for closed organ pipe = fundamental frequency for open organ pipe.
$∴ \frac{3 v}{4 l} = \frac{v}{2 l^{'}} \Rightarrow l^{'} = \frac{4 l}{3 \times 2} = \frac{2 l}{3}$
where $l$ and $l^{'}$ are the lengths of closed and open organ pipes respectively.
$∴ = \frac{2 \times 20}{3} = 13.33 cm$

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