Vibration of which among the following produces only odd harmonics?

An air column in a closed organ pipe

The correct answer is option 3. An air column in a closed organ pipe.

The vibration that produces only odd harmonics is an air column in a closed organ pipe.

Harmonics: When a vibrating system vibrates at its fundamental frequency, it can also vibrate at multiples of that frequency. These multiples are called harmonics. The first harmonic is the fundamental frequency itself, the second harmonic is twice the fundamental frequency, and so on.

Open vs. Closed Organ Pipes:

In an open organ pipe, there is an open end where the air vibrates freely. This allows for the formation of both even and odd harmonics.

In a closed organ pipe, one end is closed, and the air vibration reflects there. This specific boundary condition only allows for the formation of odd harmonics.

The other options:

Vibrating rod fixed at two ends: This produces both even and odd harmonics.

Vibrating string fixed at two ends: Similar to the rod, a string fixed at both ends also produces both even and odd harmonics.