Question

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe $L$ metre long. The length of the open pipe will be

• A. $\frac{L}{2}$
• B. $4L$
• C. $L$
• D. $2L$

Answer 1

The correct option is D $2L$

For second overtone (third harmonic) in open organ pipe,
$\frac{3\lambda }{2}=l_0\Rightarrow \lambda =\frac{2l_0}{3}$
For first overtone (third harmonic) in closed organ pipe
$\frac{3\lambda }{4}=l_C\Rightarrow \lambda =\frac{4l_C}{3}=\frac{4L}{3}$
So, $\frac{2l_0}{3}=\frac{4L}{3}\Rightarrow l_0=2L$