When testing a thick plate using longitudinal waves, a change in frequency will result in what for sound velocity?

• A. Increased sound velocity
• B. Decreased sound velocity
• C. Change in velocity with frequency
• D. No change in sound velocity

Answer: (D)

When a longitudinal wave travels through a homogeneous solid, its speed is fixed by the material’s stiffness and density, not by how high the frequency is. In elastic theory, the bulk longitudinal wave speed depends on elastic moduli (like the bulk and shear moduli) and the density, and these properties don’t change with frequency over the typical ultrasonic range. So changing the frequency changes the wavelength, but not the velocity.

In a thick plate, the wave can behave like a bulk longitudinal wave, so the plate’s boundaries have little effect on its speed. Dispersion, where velocity changes with frequency, appears for guided plate waves (Lamb waves) in thinner plates or more complex modes, not for simple bulk longitudinal waves in a thick plate. Therefore, there is no change in sound velocity with frequency.