In steel, the velocity of sound is greatest in which mode?

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

Answer: (B)

In steel, the compressional (longitudinal) wave travels the fastest. Particles move parallel to the direction of propagation, producing bulk compressions and rarefactions that use the material’s stiffness most effectively. For isotropic solids, the longitudinal speed depends on both the bulk and shear moduli and is given by v_p = sqrt((K + 4G/3)/ρ), while the shear speed is v_s = sqrt(G/ρ). Since K is larger and contributes to a higher v_p, the longitudinal wave outpaces the shear wave. Surface (Rayleigh) waves travel along the surface and are typically slower than bulk waves, so they are not the fastest. Therefore, the greatest velocity in steel is the longitudinal mode.