Q. 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
VMMC MedicalVMMC Medical 2007
Solution:
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.
