Shear Wave Velocity Calculator
Calculate shear wave velocity in materials using shear modulus and density
Calculate Shear Wave Velocity
Select a predefined material or choose "Custom Material" to enter your own values
Material's modulus of rigidity (resistance to shear deformation)
Material's mass per unit volume
Shear Wave Velocity Results
Formula used: Vs = √(G / ρ)
Input values: G = 0.00e+0 Pa, ρ = 0.0 kg/m³
Estimated longitudinal wave velocity: 0.00 m/s (≈ 2 × Vs)
Wave Classification
Example Calculation
Copper Rod Example
Material: Copper rod
Shear modulus (G): 45 GPa
Density (ρ): 8,940 kg/m³
Calculation
Vs = √(G / ρ)
Vs = √(45,000,000,000 / 8,940)
Vs = √(5,033,557)
Vs = 2,244 m/s
Types of Waves in Solids
Shear Waves (S-waves)
Particles oscillate ⊥ to propagation
Also called secondary waves
Primary Waves (P-waves)
Particles oscillate ∥ to propagation
Faster than shear waves
Rayleigh Waves
Surface waves in semi-infinite media
Elliptical particle motion
Applications
Geotechnical site evaluation
Non-destructive testing
Seismic wave analysis
Material characterization
Structural health monitoring
Understanding Shear Wave Velocity
What are Shear Waves?
Shear waves are a type of wave that occurs in bulk media when particles oscillate perpendicular to the direction of wave propagation. They are generated by shear forces acting along opposite faces of a material and cause changes in shape without volume change.
Key Characteristics
- •Also known as S-waves or secondary waves
- •Cannot propagate through liquids or gases
- •Velocity is approximately half of longitudinal waves
- •Important in seismic analysis and material testing
Formula and Theory
Vs = √(G / ρ)
- Vs: Shear wave velocity (m/s)
- G: Shear modulus or modulus of rigidity (Pa)
- ρ: Material density (kg/m³)
Physics: The velocity depends on the material's resistance to shear deformation (shear modulus) and its inertia (density). Stiffer, lighter materials have higher velocities.
Typical Material Properties
| Material | Shear Modulus (GPa) | Density (kg/m³) | Velocity (m/s) |
|---|---|---|---|
| Steel | 80 | 7,850 | 3,190 |
| Aluminum | 26 | 2,700 | 3,100 |
| Copper | 45 | 8,940 | 2,244 |
| Concrete | 15 | 2,400 | 2,500 |