What is the phase difference between the prongs of the tuning fork

The correct option is π.

To understand why the phase difference between the two prongs of a tuning fork is $\pi$ radians (or 180°), let us analyze the physical motion of a tuning fork when it vibrates to produce sound.

When a tuning fork is struck, its two prongs vibrate. Their motion is highly symmetrical:
- As one prong moves outwards to the left, the other prong simultaneously moves outwards to the right.
- Similarly, when one prong moves inwards towards the center, the other prong also moves inwards towards the center.

This means that at any given instant, the displacements of the two prongs are equal in magnitude but opposite in direction. The prongs are always moving in opposite directions relative to their equilibrium positions.

In wave mechanics, when two vibrating bodies or points in a medium move in opposite directions at the same time (one reaching its maximum positive displacement while the other reaches its maximum negative displacement), they are said to be in opposite phases, or completely out of phase.

A complete cycle of vibration corresponds to a phase angle of 2$\pi$ radians (360°). Since the two prongs are always in exactly opposite states of motion, they are half a cycle out of phase.
Therefore, the phase difference $\mathrm{\Delta \varphi }$ between them is given by:

$\mathrm{\Delta \varphi }=\frac{1}{2}\times 2\pi =\pi$

Thus, the phase difference between the prongs of the tuning fork is $\pi$ radians.