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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
Explanation
Equate $\frac{3v}{4l}$ (closed) with $\frac{v}{2l'}$ (open) to get $l' = \frac{2l}{3}$.
Detailed Solution
For the closed organ pipe, third harmonic $= \frac{3v}{4l}$
For the open organ pipe, fundamental frequency $= \frac{v}{2l'}$
Given, $\frac{3v}{4l} = \frac{v}{2l'}$
$\Rightarrow l' = \frac{4l}{3\times 2} = \frac{2l}{3}$
$= \frac{2\times 20}{3} = 13.33$ cm
So the length of the open organ pipe is about 13.3 cm (the listed value 13.2 cm).
Note: the exact calculation gives 13.33 cm; the official key marks 13.2 cm as the nearest option.