Question

The fundamental frequency of a closed organ pipe is n. Its length is doubled and radius is halved. Its frequency will become nearly.

• A. $\frac{n}{2}$
• B. $\frac{n}{3}$
• C. $n$
• D. $2n$

Answer 1

The correct option is A $\frac{n}{2}$

We know, $f_n=\frac{nv}{2(L+1.4D)}$ for an open pipe, and $f_n=\frac{(2n-1)v}{4(L+D)}$ for closed pipes.

Where, $n$ is an integer, $v=$ Speed of light, $L=$ length of the pipe, $D=$ diameter of the pipe.

In the stated problem we have closed pipe where in the second case L becomes $2L$ and $D$ becomes $D/2$.
Putting these values we get frequency will become nearly half.