Question

An organ pipe of length $L$ is open at one end and closed at the other. What are the wavelengths corresponding to the three lowest frequencies that can be produced with this pipe?

• A. $4L,2L,L$
• B. $2L,L,\frac{L}{2}$
• C. $2L,L,\frac{2L}{3}$
• D. $4L,\frac{4L}{3},\frac{4L}{5}$

Answer 1

The correct option is D $4L,\frac{4L}{3},\frac{4L}{5}$

For $n^{\text{th}}$ over tone
$n\frac{\lambda }{2}+\frac{\lambda }{4}=L$
$(2n+1)\frac{\lambda }{4}=L$
$\Rightarrow \lambda =\frac{4L}{2n+1}$
As $n$ increases frequency increases.
3 wavelengths, $n=0,n=1,n=2$
$\lambda =4L,\frac{4L}{3},\frac{4L}{5}$