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

Answer

B

Explanation

Four the closed pipe of length `l_(c)`, the fundamental frequency ` = v/(4l_(c)) `
and for the open pipe, of length `l_(o)`, the fundamental frequency ` = v/(2l_(o))`
` :. ` The frequency of the second overtone of the open pipe ` = (3v)/(2l_(o))`
It is given that ` v/(4l_(c)) = (3v)/(2l_(o)) `
` :. l_(o) = 6l_(c) = 6 xx 20 = 120 ` cm