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

Options

A. 13.2 cm
B. 8 cm
C. 12.5 cm
D. 16 cm

Explanation

For closed organ pipe, third harmonic is `(3v)/(4l)`
For open organ pipe, fundamental frequency is `(v)/(2l.)`
Given, third harmonic for closed organ pipe = fundamental frequency for open organ pipe.
`therefore (3v)/(4l)=(v)/(2l.)impliesl.=(4l)/(3xx2)=(2l)/(3)`
where l and l. are the lengths of closed and open organ pipes respectively.
`therefore l.=(2xx20)/(3)=13.33cm`