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 the length \( L \) of the pipe and the harmonic number \( n \) is given by: \[ L = \frac{(2n-1)\lambda}{4}, \] where \( \lambda \) is the wavelength of the sound. For the third overtone, we have: \[ n = 4. \] This corresponds to the 4th harmonic, which has 4 nodes and 4 antinodes, with the pattern of oscillation as follows: - The pipe has four full loops, plus a half loop. - This results in 4 nodes and 4 antinodes. Final Answer: \[ \boxed{\text{Four nodes and four antinodes}}. \]