Amplitude of vibration of any particle in a standing wave produced along a stretched string depends on the location of the particle.

Explanation:
A standing wave is formed when two waves of the same frequency and amplitude traveling in opposite directions superpose. In a standing wave, there are specific points called nodes and antinodes. The nodes are stationary points where the particles do not vibrate, while the antinodes are points of maximum displacement where the particles vibrate with maximum amplitude.

The amplitude of vibration of any particle in a standing wave is determined by its location along the string. This can be understood by considering the behavior of particles at different locations in the standing wave.

Nodes:
At the nodes of the standing wave, the particles do not vibrate at all. They remain stationary and have zero amplitude of vibration. The nodes are formed at regular intervals along the string, and the particles located at these nodes experience no displacement from their equilibrium position.

Antinodes:
At the antinodes of the standing wave, the particles vibrate with maximum amplitude. The antinodes are formed at the points of maximum displacement, and the particles located at these points experience the maximum amount of displacement from their equilibrium position.

Variation in Amplitude:
As we move from a node to an adjacent antinode along the string, the amplitude of vibration of the particles increases gradually. The particles located closer to the antinodes experience a larger displacement and hence have a larger amplitude of vibration. On the other hand, the particles located closer to the nodes have a smaller displacement and hence a smaller amplitude of vibration.

Therefore, the amplitude of vibration of any particle in a standing wave produced along a stretched string depends on its location. The particles located at the antinodes have maximum amplitude of vibration, while the particles located at the nodes have zero amplitude of vibration. The amplitude gradually increases as we move from the nodes towards the antinodes along the string.