Question

A closed organ pipe (closed at one end) is excited to support the third overtone. It is found that air in the pipe has:

• A. Three nodes and three antinodes
• B. Three nodes and four antinodes
• C. Four nodes and three antinodes
• D. Four nodes and four antinodes

Hint:

In a closed organ pipe, the number of nodes and antinodes increases with the overtone number. For the third overtone (fourth harmonic), the pipe supports four nodes and four antinodes.

Answer 1

The Correct Option is D

For a closed organ pipe, the relationship between pipe length \( L \) and harmonic number \( n \) is \( L = \frac{(2n-1)\lambda}{4} \), where \( \lambda \) is the sound's wavelength. For the third overtone, \( n = 4 \). This corresponds to the 4th harmonic, characterized by 4 nodes and 4 antinodes. The oscillation pattern consists of four full loops and one half loop, resulting in 4 nodes and 4 antinodes. Final Answer: \[ \boxed{\text{Four nodes and four antinodes}}. \]