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

Solution

$\text{For closed organ pipe, third harmonic is}\frac{3v}{4l}$

$\text{For open organ pipe, fundamental frequency is}\frac{v}{2{l}^{\text{'}}}$

Given, third harmonic for closed organ pipe = fundamental frequency for open organ pipe.

$\therefore \frac{3v}{4l}=\frac{v}{2{l}^{\text{'}}}\Rightarrow {l}^{\text{'}}=\frac{4l}{3\times 2}=\frac{2l}{3}$

where $l$ and ${l}^{\mathit{\text{'}}}$ are the lengths of closed and open organ pipes respectively.

$\therefore =\frac{2\times 20}{3}=13.33\mathrm{cm}$

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