How is the speed of sound in a solid calculated?

The calculator uses the formula v = sqrt(E / ρ), where v is the speed, E is Young's modulus in pascals (Pa), and ρ is density in kg/m³. Enter these values to get the longitudinal wave speed.

What units should I use for Young's modulus and density?

Young's modulus must be in pascals (Pa) and density in kilograms per cubic meter (kg/m³). If your values are in other units, convert them first to ensure accurate results.

Does this calculator work for all solids?

It works for isotropic solids where longitudinal wave speed depends on Young's modulus and density. For anisotropic materials or non-ideal conditions, results may vary.

Physics

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Speed of Sound in Solids Calculator.

Calculate longitudinal wave speed from Young's modulus and density.

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02 / ANSWER

Young's modulus

Density

Speed

5,047.544651m/s

Results update automatically as you type.

Use Cases

Engineering material selection

Compare sound speeds in different materials to choose suitable ones for acoustic applications or structural design.

Example: Compare steel (E=200 GPa, ρ=7850 kg/m³) vs aluminum (E=69 GPa, ρ=2700 kg/m³).

Physics education and experiments

Verify theoretical values in lab experiments or homework problems involving wave propagation in solids.

Example: Calculate the speed in a copper rod with E=110 GPa and ρ=8960 kg/m³.

Frequently Asked Questions

How is the speed of sound in a solid calculated?: The calculator uses the formula v = sqrt(E / ρ), where v is the speed, E is Young's modulus in pascals (Pa), and ρ is density in kg/m³. Enter these values to get the longitudinal wave speed.
What units should I use for Young's modulus and density?: Young's modulus must be in pascals (Pa) and density in kilograms per cubic meter (kg/m³). If your values are in other units, convert them first to ensure accurate results.
Does this calculator work for all solids?: It works for isotropic solids where longitudinal wave speed depends on Young's modulus and density. For anisotropic materials or non-ideal conditions, results may vary.

Tips & Common Mistakes

Tips

Ensure Young's modulus is in pascals (Pa); 1 GPa = 1e9 Pa.
Use consistent units: density in kg/m³ and modulus in Pa for speed in m/s.
For accurate results, use material property values from reliable sources, as they can vary with temperature and composition.
Remember this formula assumes a homogeneous, isotropic solid and neglects effects like damping or temperature.

Common Mistakes to Avoid

Forgetting to convert GPa to Pa (multiply by 1e9) before entering Young's modulus.
Using density in g/cm³ instead of kg/m³ (multiply by 1000 to convert).
Mixing up units or entering values in different unit systems without conversion.

Last updated: August 13, 2026