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

Options

A. 120 cm
B. 140 cm
C. 80 cm
D. 100 cm

Explanation

For closed organ pipe, fundamental frequency is given by
`upsilon_(c)=(v)/(4l)`
For open organ pipe, fundamental frequency is givne by
`upsilon_(o)=(v)/(2l.)`
`2^(nd)` overtone of open organ pipe `upsilon.=3upsilon_(o),upsilon.=(3v)/(2l.)`
According to question, `upsilon_(c)-upsilon.`
`(v)/(4l)=(3v)/(2l.)`
`l.=6l`
Here, `l=20cm, l.=? therefore l.=6xx20=120cm`