Question

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

Answer 1

The correct option is D

120 cm

For closed organ pipe fundamental frequency

$n_1=\frac{v}{4l_1}$

For open organ pipe fundamental frequency

$n_2=\frac{v}{2l_2}$

The second overtone is

$n_2^1=3.n_2=\frac{3v}{2l_2}$
$n_2^1=n_1$
$\frac{3v}{2l_2}=\frac{v}{4l_1}\therefore l_2=6l_1=6\times 20=120cm.$