Question

when the density of the medium increases the wave speed increases/decreases evidence from the data

Answer 1

Short answer: It depends on the type of wave and what else changes with density.

Explanation and evidence:

1) Waves on a stretched string (or similar 1-D mechanical media)
- Formula: v = sqrt(T/μ) where T is tension and μ is linear mass density.
- If μ increases while T is fixed, v decreases (v ∝ 1/√μ).
- Numerical example: T = 100 N, μ = 0.01 kg/m → v = sqrt(100/0.01) = 100 m/s. If μ doubles to 0.02 kg/m → v = sqrt(100/0.02) ≈ 70.7 m/s (speed falls by factor 1/√2).

2) Sound waves in fluids and solids
- Formula (fluids): v = sqrt(B/ρ) where B is the bulk modulus and ρ is density. (For longitudinal waves in solids a similar form v ≈ sqrt(E/ρ) with Young’s modulus E.)
- If B (or E) is held constant, increasing ρ makes v decrease (v ∝ 1/√ρ).
- However, in real materials B or E usually change together with ρ. Stiffer materials tend to be denser, and stiffness often increases faster than density, so v can increase with density when you compare different media.

Evidence from measured data (typical values)
- Air (ρ ≈ 1.2 kg/m³): v_sound ≈ 343 m/s
- Water (ρ ≈ 1000 kg/m³): v_sound ≈ 1480 m/s
- Steel (ρ ≈ 7800 kg/m³): v_sound ≈ 5,000–6,000 m/s

These data show that although density increases by many orders of magnitude from air → water → steel, wave speed also increases because the bulk/elastic moduli increase far more strongly than density.

Conclusion
- If you hold the medium’s stiffness constant and only increase density, wave speed decreases.
- When comparing different materials, increased density often comes with much greater stiffness, and the net effect is an increase in wave speed (as seen in air → water → steel).