Which vibration mode propagates fastest in solids, explaining velocity differences?

Which vibration mode propagates fastest in solids, explaining velocity differences?

• A. Longitudinal
• B. Surface wave
• C. Sound velocity identical in all modes
• D. Shear

Answer: (A)

In solids, the fastest vibration mode is the longitudinal (compressional) wave. This mode involves particles moving back and forth along the direction of travel, producing alternating compression and expansion. The material resists compression with its bulk modulus, and the overall restoring effect combines both bulk and shear stiffness, giving a higher phase velocity. A handy relationship shows the longitudinal speed as v_long = sqrt((K + 4/3 G)/rho). The shear wave speed is v_shear = sqrt(G/rho). Since K + 4/3 G is greater than G for any solid, the longitudinal wave travels faster. Surface (Rayleigh) waves travel along the surface and have speeds roughly 0.9 times the shear speed, so they are slower than the bulk longitudinal wave.

In solids, the fastest vibration mode is the longitudinal (compressional) wave. This mode involves particles moving back and forth along the direction of travel, producing alternating compression and expansion. The material resists compression with its bulk modulus, and the overall restoring effect combines both bulk and shear stiffness, giving a higher phase velocity. A handy relationship shows the longitudinal speed as v_long = sqrt((K + 4/3 G)/rho). The shear wave speed is v_shear = sqrt(G/rho). Since K + 4/3 G is greater than G for any solid, the longitudinal wave travels faster. Surface (Rayleigh) waves travel along the surface and have speeds roughly 0.9 times the shear speed, so they are slower than the bulk longitudinal wave.