In general, the velocity of a wave does not depend on the amplitude of the wave. The velocity of a wave is determined by the properties of the medium through which it propagates and is not directly influenced by the wave's amplitude.
The velocity of a wave is typically determined by two main factors: the properties of the medium and the wavelength of the wave. For example, in the case of a wave traveling through a uniform medium, such as a wave on a string or a sound wave in air, the velocity of the wave is determined by the tension in the string or the properties of the medium (such as density and elasticity) for sound waves.
The amplitude of a wave refers to the maximum displacement or disturbance of the wave from its equilibrium position. It represents the magnitude of the oscillation of the wave. While the amplitude of a wave affects other aspects of the wave, such as its energy or intensity, it does not directly impact the velocity of the wave.
However, there are some special cases where the amplitude of a wave can affect its velocity indirectly. For example, in certain nonlinear systems, such as water waves in shallow water or nonlinear optics, where the wave amplitude becomes large, nonlinear effects can become significant and influence the wave's behavior, including its velocity. But in most common linear systems, the velocity of a wave is not dependent on its amplitude.