Question

if wave traveled through a medium denser than steel what would you predict about its wave speed

Answer 1

Short answer: usually slower. For mechanical waves the speed depends on both the material's stiffness and its density; inertia (higher ρ) tends to slow the wave while stiffness (elastic moduli) tends to speed it up.

Key formulas:
- Fluids (sound): c = sqrt(K/ρ) where K is the bulk modulus.
- Solids (approx. longitudinal): c ≈ sqrt(E/ρ) or more precisely c_L = sqrt((K + 4/3 G)/ρ), with E = Young's modulus, G = shear modulus.
- Shear waves in solids: c_S = sqrt(G/ρ).

Implication: if you increase density while keeping the elastic moduli fixed, v scales as 1/√ρ, so a denser medium gives a lower wave speed. Example: doubling the density (with the same stiffness) reduces speed by factor 1/√2 ≈ 0.707.

Caveat: many real materials that are denser than steel are also stiffer, so whether the wave is faster or slower depends on the ratio stiffness/ρ. For electromagnetic waves, speed in a material is set by permittivity and permeability (index of refraction); denser matter often gives a higher refractive index and thus slower light, but density alone is not the sole determinant.