Of the following sound wave modes, which one has multiple or varying wave velocities?

• A. Lamb waves
• B. Longitudinal waves
• C. Shear waves
• D. Transverse waves

Answer: (A)

Dispersion of guided waves in a plate is being tested here. Lamb waves in thin plates are inherently dispersive, meaning their speed depends on frequency and on which mode you’re looking at. Because the plate geometry and free-surface boundary conditions create multiple allowable wave modes (symmetric and antisymmetric Lamb modes), each mode has its own dispersion relation. At a given frequency there can be several Lamb modes, each traveling at a different phase (and group) velocity. That gives you multiple or varying velocities.

In contrast, longitudinal and shear (transverse) waves in a uniform bulk material have a single characteristic speed for a given material—these speeds don’t vary with frequency in the same way, so they aren’t dispersive like Lamb waves in a plate.