Solids carry sound much faster than air – about 6 km/s in steel. Ultrasonic testing of welds, seismology and musical instrument design rely on these speeds. A bulk solid carries two kinds of waves: compression (longitudinal) and shear.
How to use the Speed of Sound in Solids Calculator
- Material
- Young’s modulus E
- Density ρ
- Poisson’s ratio ν
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Pick a material or choose Custom and enter its elastic properties.
Inputs explained
| Field | What to enter |
|---|---|
| Material | Choose one: Structural steel, Stainless steel, Aluminium, Copper … |
| Young’s modulus E | Units: GPa, MPa, Pa, psi, Mpsi |
| Density ρ | Units: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³ |
| Poisson’s ratio ν | A number |
What each result means
- Longitudinal wave speed = sqrt([E]×(1 – [nu])÷([rho]×(1 + [nu])×(1 – 2×[nu])))
- Shear wave speed = sqrt([E]÷(2×(1 + [nu]))÷[rho])
- Thin rod (bar) speed = sqrt([E]÷[rho])
- Shear modulus = [E]÷(2×(1 + [nu]))÷1e9
Example values
How the main result changes when Young’s modulus E changes and everything else stays at the example values above:
| Young’s modulus E (GPa) | Longitudinal wave speed (km/s) |
|---|---|
| 100 | 5.7782 |
| 150 | 5.7782 |
| 200 | 5.7782 |
| 250 | 5.7782 |
| 300 | 5.7782 |
| 400 | 5.7782 |
Formula
v_L = √(E(1 − ν) / (ρ(1 + ν)(1 − 2ν))), v_S = √(G/ρ), G = E/(2(1 + ν)), v_rod = √(E/ρ)
Worked example
Inputs — Material: Structural steel.
Results — Longitudinal wave speed = 5.77816 km/s; Shear wave speed = 3.14246 km/s; Thin rod (bar) speed = 5.04754 km/s; Shear modulus = 77.5194 GPa.
Key terms
- Poisson's ratio
- Ratio of lateral to axial strain.
Frequently asked questions
Why is sound faster in steel than in air?
Steel is enormously stiffer, which outweighs its higher density.
What is the difference between P and S waves?
P waves compress the material; S waves shear it and are slower.
Why does a thin rod have a different speed?
It can expand sideways, so it is effectively less stiff.
How is this used in practice?
Ultrasonic flaw detection and seismology.