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The fundamental frequency in an open org...

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

A

12 . 5 cm

B

8 cm

C

13 . 2 cm

D

16 cm

Text Solution

Verified by Experts

The correct Answer is:
C
Third harmonic of a closed organ pipe,
`n_(2) = (3V)/(4l) ` [ l = length of closed organ pipe V = velocity of sound]
Fundamental frequency of open organ pipe,
`n_(0) = (V)/(2l^(.)` [`l^(.) = ` length of open organ pipe]
`:.(3V)/(4l)=(V)/(2l^(.))or, l^(.) = (4l)/(3xx2) = (2l)/(3) = (2xx20)/(3)`
or, `l^(.) = 13 . 33` cm
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