Acoustic velocities in materials are primarily governed by which properties?

• A. Density
• B. Elasticity
• C. Both A and B
• D. Acoustic impedance

Answer: (C)

Acoustic velocity is set by how stiff a material is and how much mass it has to move. The stiffness, from elastic moduli, provides the restoring force that carries the wave, while density provides the inertia that the wave has to accelerate as it propagates. In isotropic solids, compressional wave speed grows with stiffness and decreases with density, roughly v_p = sqrt((K + 4/3 μ)/ρ), and shear wave speed is v_s = sqrt(μ/ρ). In liquids, the speed is v = sqrt(B/ρ), with B as the bulk modulus. So increasing stiffness raises velocity, while increasing density lowers it. Acoustic impedance, Z = ρ v, ties the two together but does not determine velocity by itself.