Final answer:
The velocity of a wave in a medium changes only if there is a change in the properties of the medium itself, such as density or temperature. The wave speed is constant in a specific medium, but the individual particles in the medium have varying velocities as they oscillate.
Step-by-step explanation:
The velocity of a wave traveling in a medium changes only if a property of the medium changes. This is because a wave's speed depends on the properties of the material through which it is traveling. Changes in the wave property such as frequency don't affect the velocity of the wave in a given medium but can change the wavelength. The speed of a wave is determined by the medium's properties such as density and elasticity, not by the wave's frequency or wavelength. For sound waves, for example, the speed is primarily dependent on the medium's properties like density and temperature.
An important aspect to understand is that while the wave speed is constant in a specific medium, the velocity of the medium's particles is not constant. The particles oscillate around an equilibrium position and have their own velocity and acceleration, which is different from the wave's velocity.