Shear Wave Velocity Calculator
Calculate shear wave velocity from shear modulus and density
Material shear modulus (modulus of rigidity)
Material density (if input is in kg/m³, divide by 1000)
How to Use This Calculator
Enter Shear Modulus
Input the material's shear modulus (G), also known as the modulus of rigidity. Enter in MPa (e.g., 30000 for 30 GPa) or GPa. This represents the material's resistance to shear deformation.
Enter Density
Input the material density (ρ). The calculator assumes input in g/cm³. If you have density in kg/m³, divide by 1000 first (e.g., 7850 kg/m³ becomes 7.85 g/cm³).
Calculate Velocity
Click "Calculate" to determine the shear wave velocity (vs). The result shows both m/s and km/s. This represents how fast shear waves propagate through the material.
Formula
Shear Wave Velocity = √(Shear Modulus ÷ Density)
vₛ = √(G / ρ)
Where:
- vₛ = Shear wave velocity - m/s or km/s
- G = Shear modulus - Pa (or MPa/GPa)
- ρ = Density - kg/m³ (or g/cm³)
Note:
Ensure consistent units. The formula uses G in Pa and ρ in kg/m³. Common conversions: 1 MPa = 10⁶ Pa, 1 g/cm³ = 1000 kg/m³.
Example:
For steel with G = 80 GPa (80,000 MPa) and ρ = 7.85 g/cm³:
vₛ = √(80×10⁹ / 7850) = 3,195 m/s (3.20 km/s)
About Shear Wave Velocity Calculator
The Shear Wave Velocity Calculator is an essential tool for geophysics, seismology, and materials science that calculates the velocity of shear waves (S-waves) through a material. Shear wave velocity is a fundamental property used in seismic analysis, earthquake engineering, and non-destructive testing to characterize material properties and subsurface structures.
When to Use This Calculator
- Seismic Analysis: Calculate S-wave velocities for earthquake studies
- Geotechnical Engineering: Characterize soil and rock properties from seismic tests
- Non-Destructive Testing: Determine material properties from ultrasonic measurements
- Earth Science Research: Study wave propagation in Earth's interior
- Material Characterization: Relate elastic properties to wave velocities
Why Use Our Calculator?
- ✅ Quick Calculation: Instant shear wave velocity from modulus and density
- ✅ Geophysical Tool: Essential for seismic analysis and earthquake engineering
- ✅ Material Testing: Relate elastic properties to wave propagation
- ✅ Educational Resource: Understand wave mechanics and material properties
- ✅ Accurate Results: Precise calculations for scientific applications
Key Concepts
Shear Waves (S-waves): Transverse waves that cause particles to move perpendicular to the direction of wave propagation. Unlike compressional waves (P-waves), shear waves cannot propagate through fluids. Their velocity depends on the material's shear modulus and density.
Relationship to Material Properties: Shear wave velocity is directly related to the square root of the ratio of shear modulus to density. Higher shear modulus and lower density result in faster wave propagation. This relationship allows estimation of material properties from seismic measurements.
Typical Values
- Steel: ~3,200 m/s (3.2 km/s)
- Concrete: ~2,000-3,000 m/s
- Rock (Granite): ~3,000-4,000 m/s
- Soil (Clay): ~100-500 m/s
- Water: Cannot propagate S-waves (zero shear modulus)
Frequently Asked Questions
What is shear wave velocity?
Shear wave velocity (vₛ) is the speed at which shear waves (S-waves) propagate through a material. It is calculated as vₛ = √(G/ρ), where G is the shear modulus and ρ is the density. S-waves are transverse waves that cause particles to move perpendicular to the wave direction.
How is shear wave velocity different from P-wave velocity?
P-waves (compressional waves) travel faster than S-waves and cause particles to move parallel to the wave direction. P-wave velocity depends on bulk modulus and density, while S-wave velocity depends on shear modulus and density. P-waves can travel through fluids, but S-waves cannot.
Why can't shear waves travel through fluids?
Shear waves require the material to resist shear deformation, which requires a shear modulus. Fluids have zero (or near-zero) shear modulus because they cannot resist shear forces - they simply flow. This is why S-waves cannot propagate through liquids or gases, making them useful for detecting Earth's liquid outer core.
How is shear wave velocity used in geophysics?
Shear wave velocity is used to characterize subsurface materials, determine soil/rock stiffness, estimate earthquake ground motion, and identify subsurface structures. Seismologists use the difference between P-wave and S-wave arrival times to locate earthquakes and determine material properties at depth.
Can I use this for ultrasonic testing?
Yes! Ultrasonic testing uses the same principle - measuring wave velocities to determine material properties. By measuring shear wave velocity experimentally and knowing density, you can back-calculate the shear modulus. This is commonly used in non-destructive testing of metals, composites, and concrete.