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The fundamental frequency of a closed or...

The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

A

80 cm

B

100 cm

C

120 cm

D

140 cm

Text Solution

Verified by Experts

The correct Answer is:
C
Frequency of the fundamental tone of the closed organ pipe
`(v)/(4l) = (v)/(4 xx 20) = (v)/(80) ` [ v = velocity of sound]
If L is the length of the organ pipe open at both the ends, frequency of the fundamental tone ` = (v)/(2L) `, then the frequency of the second overtone, i.e., the third har-monic ` = (3*(v)/(2L))`
According to the question,
`(v)/(80) = 3 * (v)/(2L) or, L = (3)/(2) xx 80 = 120 ` cm
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