When testing a thick plate with longitudinal waves, changing frequency has what effect on the speed of sound in the plate?

When testing a thick plate with longitudinal waves, changing frequency has what effect on the speed of sound in the plate?

• A. Speed remains unchanged
• B. Speed increases with frequency
• C. Speed decreases with frequency
• D. Speed oscillates irregularly

Answer: (A)

In a homogeneous, nondispersive solid, the speed of a longitudinal wave is set by the material’s elastic properties and density, not by how fast the wave oscillates. The formulas for bulk longitudinal velocity depend on parameters like the elastic moduli and density, and frequency does not appear in them. So for a thick plate where the material behaves nondispersively, changing the frequency leaves the speed essentially the same. What does change with frequency is the wavelength (since λ = v/f), not the speed itself. Only if dispersion were present—such as certain guided Lamb-wave modes in plates or highly dispersive materials—would speed vary with frequency.

In a homogeneous, nondispersive solid, the speed of a longitudinal wave is set by the material’s elastic properties and density, not by how fast the wave oscillates. The formulas for bulk longitudinal velocity depend on parameters like the elastic moduli and density, and frequency does not appear in them. So for a thick plate where the material behaves nondispersively, changing the frequency leaves the speed essentially the same. What does change with frequency is the wavelength (since λ = v/f), not the speed itself. Only if dispersion were present—such as certain guided Lamb-wave modes in plates or highly dispersive materials—would speed vary with frequency.