Question

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe $2m$ long. The length of the open pipe is:

• A. $8m$
• B. $4m$
• C. $2m$
• D. $1m$

Answer 1

Answer: (B)

$4m$

Given : Length of the closed pipe $L^{\prime }=2$ m

First overtone frequency of closed pipe ${\nu }^{\prime }=\frac{3v}{4L^{\prime }}$

Let the length of the open organ pipe be $L$

Second overtone of an open pipe i.e $m=3$ ${\nu }_3=\frac{3v}{2L}$

But ${\nu }_3={\nu }^{\prime }$

$\therefore$ $\frac{3v}{2L}=\frac{3v}{4L^{\prime }}$

$⟹L=2L^{\prime }=2\times 2=4$ m