How does increasing the frequency of an ultrasonic longitudinal wave affect its velocity in a plate?

In ultrasonic testing, the velocity of a longitudinal wave in a material is determined primarily by the physical properties of that material, specifically its density and elastic modulus. The velocity of sound in a solid is given by the equation:

[ v = \sqrt{\frac{E}{\rho}} ]

where ( v ) is the velocity, ( E ) is the elastic modulus of the material, and ( \rho ) is the density.

When the frequency of the ultrasonic wave is increased, it does not affect the material properties (density and elastic modulus) that determine wave velocity. As a result, the velocity remains constant regardless of frequency changes. This principle holds true for homogeneous isotropic materials.

In practical applications, while higher frequencies may improve resolution and provide greater detail in imaging or testing, they do not influence the velocity of the wave within the material. Therefore, it is accurate to state that increasing the frequency of an ultrasonic longitudinal wave does not change its velocity in a plate.