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Question

Physics Question on 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 20cm20\,cm, the length of the open organ pipe is

A

16 cm

B

13.3 cm

C

12.5 cm

D

8 cm

Answer

13.3 cm

Explanation

Solution

For closed organ pipe, third harmonic =3v4l= \frac{3v}{4l} For open organ pipe, fundamental frequency =v2l= \frac{v}{2l'} Given, 3v4l=v2l\frac{3v}{4l} = \frac{v}{2l'} l=4l3×2=2l3\Rightarrow l' = \frac{4l}{3 \times2} = \frac{2l}{3} =2×203= \frac{2 \times20}{3} =13.33cm= 13.33\, cm