Question

Open organ pipe becomes closed. Find harmonic relation.

• A. \(n=3,\ f_2=\frac{3}{4}f_1\)
• B. \(n=5,\ f_2=\frac{3}{4}f_1\)
• C. \(n=3,\ f_2=\frac{5}{4}f_1\)
• D. \(n=5,\ f_2=\frac{5}{4}f_1\)

Hint:

Closed pipe supports only odd harmonics.

Answer 1

The Correct Option is D

Understanding the Concept: Open pipe: \[ f_1 = \frac{v}{2L} \] Closed pipe: \[ f_n = \frac{nv}{4L},\ n=1,3,5,\dots \]

Step 1: Frequency increases
\[ f_{\text{closed}}>f_{\text{open}} \]

Step 2: Match
\[ \frac{nv}{4L} = \frac{5}{4}\cdot \frac{v}{2L} \Rightarrow n=5 \]