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)

n/2

Answer 2

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 ${{l}_{2}}=2{{l}_{1}},{{r}_{2}}=\frac{{{r}_{1}}}{2},{{n}_{1}}=n$ $\Rightarrow$ $\frac{{{n}_{1}}}{{{n}_{2}}}=\frac{{{l}_{2}}}{{{l}_{1}}}$ $\Rightarrow$ ${{n}_{2}}={{n}_{1}}\frac{{{l}_{1}}}{{{l}_{2}}}=n\frac{{{l}_{1}}}{2{{l}_{1}}}=\frac{n}{2}$ Note: A closed pipe produces only odd harmonics.