Question

In a closed organ pipe, the number of nodes formed in fifth and ninth harmonics are respectively:

• A. \( 5, 9 \)
• B. \( 3, 5 \)
• C. \( 5, 7 \)
• D. \( 2, 4 \)

Hint:

For closed organ pipes, only odd harmonics exist, and the number of nodes is: \[ \frac{n + 1}{2} \] where \( n \) is the harmonic number.

Answer 1

The Correct Option is C

Step 1: Understanding Harmonics in a Closed Organ Pipe A closed organ pipe has only odd harmonics: \[ n = 1, 3, 5, 7, 9, \dots \] For the \( n \)th harmonic, the number of nodes is: \[ \frac{n + 1}{2} \] Step 2: Computing Nodes for 5th and 9th Harmonics For the 5th harmonic: \[ \frac{5 + 1}{2} = \frac{6}{2} = 3 \text{ nodes} \] For the 9th harmonic: \[ \frac{9 + 1}{2} = \frac{10}{2} = 5 \text{ nodes} \] Thus, the correct answer is: \[ 5, 7 \]