Physics
Physics
Problem
Fundamental frequency of an open organ pipe is . Match the following two columns for a closed pipe of double the length.| Column I | Column II |
|---|---|
| (a) Fundamental frequency | (p) |
| (b) Second overtone frequency | (q) |
| (c) Third harmonic frequency | (r) |
| (d) First overtone frequency | (s) None of these |
Intuitive explanation
The key is understanding how pipe geometry changes the harmonic series. An open pipe supports all harmonics (1, 2, 3, 4, ...), while a closed pipe supports only odd harmonics (1, 3, 5, 7, ...). When you double the length, the fundamental frequency halves—but then you must identify which harmonic number each term refers to, since "overtone" and "harmonic" count differently in closed pipes.
Intuitive explanation
The key is understanding how pipe geometry changes the harmonic series. An open pipe supports all harmonics (1, 2, 3, 4, ...), while a closed pipe supports only odd harmonics (1, 3, 5, 7, ...). When you double the length, the fundamental frequency halves—but then you must identify which harmonic number each term refers to, since "overtone" and "harmonic" count differently in closed pipes.