Question

which wave do you think will travel faster: a dense medium or less dense medium

Answer 1

Short answer: It depends on the type of wave and the other properties of the medium. Wave speed is controlled by both the medium’s stiffness (ability to resist deformation) and its inertia (density).

Key formulas and rules:
- Longitudinal (sound) waves in a fluid: v = sqrt(B/ρ) where B is the bulk modulus (stiffness) and ρ is density. So speed increases with higher stiffness and decreases with higher density.
- Longitudinal/transverse waves in solids: similarly v ∝ sqrt(elastic modulus/ρ) (e.g. for compressional waves in a solid v ≈ sqrt((K + 4/3 G)/ρ)).
- Transverse waves on a string: v = sqrt(T/μ) where μ is linear mass density (more mass per length → slower).
- Electromagnetic waves: v = 1/√(εμ) (in vacuum v = c); optical index n > 1 in material usually slows light relative to vacuum.

Examples:
- Air vs water vs steel (sound): water (denser than air) transmits sound faster because its bulk modulus is much larger; steel is faster still because it is much stiffer despite high density.
- A heavier string (higher μ) under the same tension carries transverse waves more slowly.
- Light travels fastest in vacuum; adding a medium (usually denser) typically slows it.

So you cannot say “denser medium always gives faster/slower waves.” The balance of stiffness (or elastic modulus) versus density determines the speed.