Table of Contents
Sound Propagation in Solids
Sound waves travel significantly faster through solids than through gases because solid materials have much higher elastic moduli (stiffness) relative to their densities. In steel, sound travels at approximately 5,050 m/s—nearly 15 times faster than in air. Diamond, the stiffest known natural material, carries sound at over 18,000 m/s.
This property is exploited in many engineering applications. Ultrasonic testing (UT) uses high-frequency sound waves to detect internal flaws in metal components. Seismology relies on the different speeds of P-waves (compressional) and S-waves (shear) through Earth's layers to map the planet's internal structure.
Formula
Where v is the longitudinal wave speed in m/s, E is Young's modulus in Pascals, and ρ is the material density in kg/m³. For a thin rod, this gives the bar velocity. For bulk materials, the formula uses the P-wave modulus: v = √((K + 4G/3) / ρ), where K is bulk modulus and G is shear modulus.
Speed in Common Solids
| Material | Speed (m/s) | E (GPa) | ρ (kg/m³) |
|---|---|---|---|
| Diamond | 18,350 | 1,220 | 3,515 |
| Steel | 5,050 | 200 | 7,850 |
| Aluminum | 5,050 | 69 | 2,700 |
| Copper | 3,610 | 117 | 8,960 |
| Glass | 5,290 | 70 | 2,500 |
| Wood (Oak) | 4,470 | 12 | 600 |
| Concrete | 3,400 | 30 | 2,400 |
Wave Types
- Longitudinal (P-waves): Particles vibrate parallel to wave direction. Fastest wave type.
- Shear (S-waves): Particles vibrate perpendicular to wave direction. ~60% of P-wave speed.
- Surface (Rayleigh): Travel along surfaces. ~90% of shear wave speed.
- Plate (Lamb): Complex waves in thin plates with both symmetric and antisymmetric modes.
Frequently Asked Questions
Why is sound faster in solids than gases?
Sound speed depends on stiffness divided by density. Although solids are denser than gases, they are enormously stiffer. Steel's Young's modulus is about 200 GPa compared to air's bulk modulus of only 0.000142 GPa. The stiffness ratio vastly exceeds the density ratio, making sound much faster in solids.
Does temperature affect sound speed in solids?
Yes, but far less than in gases. Higher temperatures slightly reduce the elastic modulus of most metals, decreasing the speed of sound by roughly 0.5-1 m/s per degree Celsius. In gases, the effect is about 0.6 m/s per degree Celsius but represents a larger percentage of the total speed.
How is this used in non-destructive testing?
Ultrasonic NDT sends sound pulses into a material and measures reflections from internal boundaries or flaws. Knowing the sound speed allows converting the round-trip time into distance, precisely locating defects like cracks, voids, or inclusions within the material.