Question

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

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

Answer 1

The correct option is B $13.2$cm

Fundamental frequency for open organ pipe is $\frac{v}{2l}$

The frequency for third harmonic for closed organ pipe is $\frac{3v}{4l_1}$

but it is given that both are equal, hence

$\frac{v}{2l}=\frac{3v}{4l_1}$

$l=\frac{2l_1}{3}$

$l=\frac{2\times 20}{3}$

$l=13.2cm$