Speed of Sound in Solids Calculator
Sound travels much faster in solids than in air — steel carries it at ~5,050 m/s, nearly 15 times faster. Select a preset material or enter Young's modulus and density to calculate the longitudinal elastic wave speed and compare it with known reference values.
Material
Longitudinal elastic wave speed: v = √(E / ρ)
- 1
Young's modulus in Pa
200 GPa × 10⁹ = 200,000,000,000 - 2
E ÷ ρ
200,000,000,000 ÷ 7,850 = 25,477,707.01 - 3
Speed of sound √(E / ρ)
√(25,477,707.01) = 5,047.5Longitudinal thin-rod wave speed
How does this calculator work?
Speed of sound in a solid thin rod = √(E/ρ), where E is Young's modulus (GPa × 10⁹) and ρ is density (kg/m³). Steel: ~5,050 m/s. Aluminium: ~5,090 m/s. Glass: ~5,290 m/s. Concrete: ~3,535 m/s. Oak: ~4,140 m/s. Lead: ~1,190 m/s. All far faster than air at 20 °C (343 m/s). Material values are typical room-temperature figures.
Formula
How this is calculated
In a solid, sound propagates as a longitudinal elastic wave: the medium alternately compresses and extends along the wave direction. The thin-rod (bar-wave) speed is v = √(E/ρ), where E is Young's modulus (Pa) and ρ is density (kg/m³). Stiffer materials carry the wave faster; denser materials slow it. This explains why steel (E ≈ 200 GPa, ρ ≈ 7,850 kg/m³, v ≈ 5,050 m/s) and glass (E ≈ 70 GPa, ρ ≈ 2,500 kg/m³, v ≈ 5,290 m/s) far outpace sound in air at 20 °C (343 m/s).
For three-dimensional bulk solids (rather than thin rods), the primary (P-wave, compressional) velocity is vP = √((K + 4G/3)/ρ), where K is the bulk modulus and G is the shear modulus. The shear (S-wave) velocity is vS = √(G/ρ). In steel, vP ≈ 5,960 m/s and vS ≈ 3,235 m/s, while the thin-rod value is ~5,050 m/s — the differences arise because a thin rod can expand laterally as it compresses longitudinally, unlike a bulk medium. This calculator uses the thin-rod formula, which is the most commonly cited and is accurate within a few percent for most engineering applications.
Practical uses include ultrasonic non-destructive testing (NDT), where pulse-echo timing locates internal flaws; seismology (P- and S-wave speeds in the Earth's crust); and sonar panel design. Material constants used here are typical room-temperature values and may vary with temperature, grain orientation, heat treatment, and alloying.
Frequently asked questions
Sound speed depends on stiffness and density. Steel is enormously stiffer than air (E ≈ 200 GPa vs air's effective bulk modulus ≈ 0.000142 GPa), so the restoring force after a small displacement is immense. Despite steel being ~6,000 times denser than air, its stiffness-to-density ratio is far higher, yielding a much faster wave.
P-waves (primary/compressional) involve compression–extension along the wave direction and travel through solids, liquids and gases. S-waves (shear) involve transverse displacement and only propagate in solids. In steel, vP ≈ 5,960 m/s and vS ≈ 3,235 m/s. This calculator gives the thin-rod longitudinal speed, which is slightly lower than vP.
Ultrasonic NDT sends a high-frequency pulse into a component and measures round-trip echo time. Distance to a flaw = v × (echo time) / 2. Knowing the material's sound speed to four significant figures lets inspectors locate defects with millimetre accuracy. Different alloys and heat treatments require individual calibration.
Also known as
TG we-Calculate Editorial Team. (2026). Speed of Sound in Solids Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/speed-sound-solids-calculator
TG we-Calculate Editorial Team. "Speed of Sound in Solids Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/speed-sound-solids-calculator.
TG we-Calculate Editorial Team, "Speed of Sound in Solids Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/speed-sound-solids-calculator
@misc{wecalculate_speed_sound_solids_calculator, title = {Speed of Sound in Solids Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/speed-sound-solids-calculator}}, year = {2026}, note = {TG we-Calculate} }
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