Speed of Sound in Solids Calculator
Calculate longitudinal and transverse sound wave speeds in solid materials using elastic properties
Calculate Sound Speed in Solids
Select a predefined material or choose custom to enter your own values
Mass per unit volume of the material
Elastic modulus (tensile stress/strain)
Modulus of rigidity (shear stress/strain)
Ratio of transverse to axial strain (0-0.5)
Sound Speed Results
Material: Steel
Density: 7850.0 kg/m³
Young's Modulus: 200.0 GPa
Acoustic Impedance: 39.62 × 10⁶ kg/(m²·s)
Wave Types
Example: Sound Speed in Copper Rod
Given Information
Material: Copper
Density (ρ): 8,940 kg/m³
Young's Modulus (E): 117 GPa
Poisson's Ratio (ν): 0.30
Calculations
1D Speed: c = √(E/ρ) = √(117×10⁹/8940) = 3,618 m/s
Longitudinal: cl = √[E(1-ν)/ρ(1+ν)(1-2ν)] = 4,197 m/s
Transverse: ct = √(G/ρ) = 2,244 m/s
Physical Interpretation
Longitudinal waves travel faster than transverse waves because compression is easier than shear deformation in solids. The 1D rod speed is between the two 3D wave speeds.
Common Materials
Values shown are approximate 1D rod speeds. Actual speeds vary with composition and temperature.
Formula Reference
1D Rod
c = √(E/ρ)
Longitudinal (3D)
cl = √[E(1-ν)/ρ(1+ν)(1-2ν)]
Transverse (3D)
ct = √(G/ρ)
E: Young's modulus
G: Shear modulus
ρ: Density
ν: Poisson's ratio
Physical Insights
Stiffness Effect
Higher elastic modulus = faster waves
Density Effect
Higher density = slower waves
Wave Order
Longitudinal > 1D Rod > Transverse
Applications
NDT, seismology, material testing
Understanding Sound Waves in Solids
Wave Types in Solids
Sound waves in solids can propagate in different modes depending on the geometry and boundary conditions. Understanding these modes is crucial for applications in non-destructive testing and seismology.
Key Factors
- •Elastic Modulus: Higher stiffness increases wave speed
- •Density: Heavier materials slow down waves
- •Poisson's Ratio: Affects 3D wave propagation
- •Geometry: Thin rods vs. bulk materials behave differently
Practical Applications
Important: Longitudinal waves (P-waves) always arrive first in seismic events because they travel faster than transverse waves (S-waves).
Mathematical Relationships
1D Rod Waves
In thin rods, only longitudinal waves can propagate effectively. The speed depends only on Young's modulus and density.
c = √(E/ρ)
Longitudinal Waves
Compression waves in bulk materials. Speed is affected by Poisson's ratio, which relates lateral to axial deformation.
cl = √[E(1-ν)/ρ(1+ν)(1-2ν)]
Transverse Waves
Shear waves that cause particles to oscillate perpendicular to wave direction. Speed depends on shear modulus.
ct = √(G/ρ)