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Elastic Solid Shear Wave Speed

Relate shear modulus, density and shear wave speed in a homogeneous linear elastic solid.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A shear modulus of 1 MPa and mass density of 1,000 kg/m³ give a shear wave speed of √1,000 m/s, approximately 31.623 m/s.

Shear wave speed = √(shear modulus / mass density)

Worked example

Enter these known values and leave the other values blank.

Illustrative material preset
Custom
Shear modulus
1 MPa
Mass density
1000 kg/m³
Shear wave speed
31.62 m/s

Assumptions and limitations

  • Modulus, density and speed must be positive. The formula assumes a homogeneous isotropic linear elastic continuum.
  • Named material presets are fixed illustrative modulus/density pairs. Composition, temperature, processing and frequency can change measured values; use Custom for known properties.
  • This predicts bulk shear wave speed, not compressional, surface or guided-wave speed. Ordinary fluids do not support this elastic bulk-shear model.

Common questions

What happens if shear modulus quadruples?

With density fixed, predicted shear wave speed doubles.

Can speed and density determine modulus?

Within this model, yes: shear modulus equals density multiplied by shear wave speed squared.

References

Pounds-force per square inch use the exact international pound and inch with standard gravity, replacing the rounded captured factor. Bookify uses exact customary mass and volume definitions for density units, replacing rounded factors in the reference.

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