Longitudinal vibrations

Longitudinal vibrations refer to the type of mechanical vibrations in which the particles of a body move parallel to its axis. In simple terms, the motion of the particles is in the same direction as the direction of propagation of the wave.

Explanation:
To understand why the correct answer is option 'B' (parallel to its axis), let's consider a simple example. Imagine a long, slender rod that is clamped at one end and free at the other end. When this rod is excited, it starts to vibrate.

Now, if we observe the motion of particles along the length of the rod, we will notice that they move back and forth in the same direction as the motion of the wave. This means that the particles move parallel to the axis of the rod.

This type of vibration is referred to as longitudinal vibrations because the particles of the body vibrate longitudinally along the axis of the body.

Perpendicular to its axis:
If the particles of a body move perpendicular to its axis, it would be considered as transverse vibrations. In transverse vibrations, the particles move perpendicular to the direction of propagation of the wave.

In a circle about its axis:
If the particles of a body move in a circle about its axis, it would be considered as torsional vibrations. Torsional vibrations involve twisting or rotation of the body about its axis.

None of the mentioned:
This is not the correct answer because longitudinal vibrations do occur when the particles of a body move parallel to its axis. Therefore, the correct answer is option 'B' (parallel to its axis).

In conclusion, longitudinal vibrations occur when the particles of a body move parallel to its axis. This type of vibration is commonly observed in various mechanical systems, such as rods, bars, and springs. Understanding the direction of particle motion is crucial in analyzing and characterizing different types of vibrations.