Among the principal wave types in metals, which has the highest velocity?

• A. Shear
• B. Surface wave
• C. Longitudinal
• D. None of the above

Answer: (C)

In metals, the speed of an elastic wave depends on how the material resists different kinds of deformation. The longitudinal (compressional) wave moves by alternating compression and expansion along the direction of travel, so its speed is set by the material’s bulk modulus and density. In an isotropic solid, its speed is v_L = sqrt((K + 4/3 μ)/ρ), where K is the bulk modulus and μ is the shear modulus. Shear waves, which move particles perpendicular to the direction of travel, depend only on the shear modulus: v_S = sqrt(μ/ρ). Since K is large in metals and both moduli are positive, v_L is greater than v_S. Surface (Rayleigh) waves travel along the surface and typically have speeds below the bulk longitudinal speed. So, the fastest of the principal wave types in metals is the longitudinal wave.