Speed of Sound in Solids
Elastic waves in solids include longitudinal (P), shear (S), and Rayleigh surface waves. Velocities depend on Young's modulus, shear modulus, Poisson ratio, and density. Used in ultrasonic NDT and material testing.
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Steel: Vโ ~5960 m/s, Vโ ~3260 m/s. Aluminum: Vโ ~6320 m/s, Vโ ~3130 m/s. Pulse-echo: thickness = v ร t/2. NDT uses longitudinal for thickness gauging.
Ready to run the numbers?
Why: Ultrasonic NDT uses wave velocities to measure thickness, detect flaws, and characterize materials. Different wave types penetrate differently.
How: Longitudinal waves are fastest; shear waves ~55% of longitudinal. Rayleigh waves travel along surfaces. Velocities come from elastic moduli and density.
Run the calculator when you are ready.
๐ง Calculation Mode
๐ Parameters
ฮป Longitudinal
5.8564 mm
ฮป Shear
3.1319 mm
๐ Visualizations
๐ Wave Types
๐ Velocity Ratios
โ๏ธ Material Comparison
๐ก Insights
Metals typically have high acoustic velocities and low attenuation
Suitable for ultrasonic NDT at MHz frequencies
At 1.00 MHz: ฮป = 5.8564 mm
Longitudinal/Shear ratio: 1.870
๐ Step-by-Step
Material: Steel (mild)
Category: Metal
Young's Modulus (E): 200.00 GPa
Shear Modulus (G): 77.00 GPa
Bulk Modulus (K): 166.67 GPa
Poisson's Ratio (ฮฝ): 0.3000
Density (ฯ): 7850 kg/mยณ
Longitudinal (P-wave): Vโ = โ[E(1-ฮฝ)/(ฯ(1+ฮฝ)(1-2ฮฝ))]
Vโ = 5856 m/s
Shear (S-wave): Vโ = โ(G/ฯ) = 3132 m/s
Rayleigh (surface): Vแตฃ โ 2905 m/s
Bar/Rod: Vbar = โ(E/ฯ) = 5048 m/s
Acoustic Impedance: Z = ฯ ร Vโ = 45.97 MRayl
Vโ/Vโ ratio: 1.8699
Longitudinal wavelength: 5.8564 mm
Shear wavelength: 3.1319 mm
For educational and informational purposes only. Verify with a qualified professional.
๐ฌ Physics Facts
Longitudinal (P) waves: particles parallel to propagation
โ Elasticity
Shear (S) waves: particles perpendicular, ~55% of P speed
โ Elasticity
Rayleigh waves: surface waves, ~90% of shear speed
โ Surface acoustics
NDT: pulse-echo measures thickness from travel time
โ Ultrasonics
What are Elastic Waves in Solids?
In solids, sound propagates as elastic waves through the material. Unlike fluids, solids support both compression (longitudinal) and shear waves due to their rigidity. The wave velocities depend on the material's elastic moduli and density.
Longitudinal (P-waves)
Particles move parallel to wave direction. Fastest wave type in solids.
Shear (S-waves)
Particles move perpendicular to wave direction. ~55% of longitudinal speed.
Rayleigh (Surface)
Surface waves with elliptical motion. ~90% of shear wave speed.
Common Materials - Acoustic Velocities
| Material | Vโ (m/s) | Vโ (m/s) | ฯ (kg/mยณ) |
|---|---|---|---|
| Steel (mild) | 5856 | 3132 | 7850 |
| Steel (stainless 304) | 5699 | 3041 | 8000 |
| Aluminum (6061) | 6153 | 3103 | 2700 |
| Aluminum (pure) | 6451 | 3103 | 2700 |
| Copper (pure) | 4399 | 2216 | 8960 |
| Brass (70/30) | 4338 | 2083 | 8530 |
| Titanium (Ti-6Al-4V) | 6294 | 3116 | 4430 |
| Cast Iron (gray) | 4122 | 2357 | 7200 |
Applications
Ultrasonic NDT
Non-destructive testing for defects, thickness measurement, weld inspection
Seismology
Earthquake wave propagation, Earth structure analysis
Medical Imaging
Ultrasound diagnostics, bone density assessment
Frequently Asked Questions
What is the difference between longitudinal and shear wave speeds?
Longitudinal (P-waves) have particles moving parallel to wave direction and are fastest. Shear (S-waves) have particles moving perpendicular and are typically ~55% of longitudinal speed. Longitudinal waves exist in all materials, while shear waves only exist in solids.
Why does wave speed depend on material properties?
Wave speed depends on elastic moduli (Young's modulus E, shear modulus G) and density ฯ. Higher modulus and lower density increase speed. The relationship is V = โ(E/ฯ) for bar waves and V = โ(G/ฯ) for shear waves.
What is Rayleigh wave speed and when is it used?
Rayleigh waves are surface waves with elliptical particle motion. They travel along material surfaces and are ~90% of shear wave speed. Used in seismology, surface acoustic wave (SAW) devices, and ultrasonic surface inspection.
How does temperature affect wave speed in solids?
Temperature affects elastic moduli and density. Generally, higher temperatures decrease moduli (materials become softer), reducing wave speeds. For metals, wave speed decreases ~0.1-0.2% per 10ยฐC increase. Critical for precision NDT measurements.
What is acoustic impedance and why is it important?
Acoustic impedance Z = ฯV is the product of density and wave velocity. It determines wave reflection/transmission at interfaces. Matching impedances minimizes reflection, important for ultrasonic transducers, medical imaging, and NDT coupling.
How accurate are these calculations for real materials?
Calculations assume isotropic, homogeneous materials. Real materials may have anisotropy, grain structure, defects, and residual stress affecting wave speeds. For critical applications, measure actual wave speeds using ultrasonic testing rather than relying solely on calculated values.
What frequency should I use for ultrasonic testing?
Higher frequencies (1-10 MHz) provide better resolution but higher attenuation. Lower frequencies (0.5-2 MHz) penetrate deeper. Choose based on material thickness: wavelength should be < thickness/10 for good resolution. Typical NDT uses 2.25-5 MHz for metals.
Can I use this calculator for thickness measurement?
Yes, use pulse-echo mode. Enter pulse-echo time (round-trip) and material. Thickness = (V ร t) / 2. Ensure you know the correct wave speed for your material and temperature. Calibrate with known thickness standards for best accuracy.
๐ Official Data Sources
โ ๏ธ Disclaimer: This calculator provides estimates based on standard material formulas and typical property values. Actual wave speeds depend on material grade, heat treatment, temperature, microstructure, and test conditions. Always consult material datasheets and testing standards (ASTM, ISO) for critical applications. Not a substitute for professional ultrasonic testing and material characterization.
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