Free · Physics models
Elastic Wave Speeds in a Solid
Compare longitudinal rod, bulk longitudinal and shear speeds in an isotropic elastic solid.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
At E = 1 GPa, density 1,000 kg/m³ and ν = 0.25, rod speed is 1,000 m/s, bulk longitudinal speed about 1,095.45 m/s and shear speed about 632.46 m/s.
crod = √(E/ρ); clong = √[E(1−ν)/(ρ(1+ν)(1−2ν))]; cshear = √[E/(2ρ(1+ν))].
Worked example
Enter these known values and leave the other values blank.
- Density of material (ρ)
- 1000 kg/m³
- Modulus of elasticity (E)
- 1 GPa
- Poisson's ratio (ν)
- .25
- Shear modulus (G)
- 0.4 GPa
- Speed (c)
- 1000 m/s
- Longitudinal speed of sound (cₗ)
- 1095.4 m/s
- Transverse speed of sound (cₜ)
- 632.5 m/s
Assumptions and limitations
- Isotropic, homogeneous, linear elastic solid. Geometric rod motion and bulk longitudinal motion have different constraints and speeds.
- The retained material presets are approximate; elastic properties depend on composition and conditions.
- The retained Poisson domain is strictly between zero and 0.5; auxetic materials are outside this calculator’s supported domain.
- Enter known quantities and clear the unknown to use available inverse branches. Locks retain supplied values. Consistency messages cover fully visible equations; identities with hidden dependencies may require a manual consistency check. Preset values are illustrative approximations, and unit selectors preserve the underlying quantity.
Common questions
How do I solve for a different quantity?
Clear that quantity and supply enough independent known values. Some outputs are one-way or tied to a selected preset, so they cannot determine every input.
References
Explicit physical domains for retained model.