Question

The frequency of vibrating air column in closed organ pipe is n. If its length be doubled and radius halved, its frequency will be nearly

• A. n
• B. n/2
• C. 2 n
• D. 4 n

Answer 1

Answer: (B)

Key Idea: Closed organ pipe has an antinode at its open end, and node at closed end. The distance between a node and antinode in closed pipe,
$\lambda /4=l$ $\Rightarrow$ $\lambda =4l$ Fundamental frequency or the first harmonic of closed pipe is $n=\frac{v}{\lambda }$ $\therefore$ $n=\frac{v}{4l}$ When $l_2=2l_1,r_2=\frac{r_1}{2},n_1=n$ $\Rightarrow$ $\frac{n_1}{n_2}=\frac{l_2}{l_1}$ $\Rightarrow$ $n_2=n_1\frac{l_1}{l_2}=n\frac{l_1}{2l_1}=\frac{n}{2}$ Note: A closed pipe produces only odd harmonics.