Question 438: Waves

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

Accepted Answer

For closed organ pipe, third harmonic
n = $${{\left( {2N - 1} ight)V} \over {4l}} = {{3V} \over {4l}}$$ ($$ \because $$ N = 2 )
For open organ pipe, fundamental
frequenty
n = $${{NV} \over {2l}} = {V \over {2l'}}$$ ($$ \because $$ N = 1 )
Given, third harmonic for closed organ pipe
= fundamental frequency for open organ pipe.
$$ 	herefore $$ $${{3V} \over {4l}} = {V \over {2l'}}$$
$$ \Rightarrow $$
l'
= $${{4l} \over {3 	imes 2}}$$ = $${{2l} \over 3}$$ = $${{2 	imes 20} \over 3}$$ = 13.33 cm

Answer

13.2 cm

Answer

8 cm

Answer

12.5 cm

Answer

16 cm

Waves

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

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