Waveform Animation (Real-time)
t = 0.00 μs
P-wave (Longitudinal / Compressional)
S-wave (Shear / Transverse)
Calculation Summary
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cP [m/s]
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cS [m/s]
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λP [mm]
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λS [mm]
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Z [MRayl]
Theory Notes — Elastic Wave Speeds
Elastic wave speeds in solids are determined by the material's elastic constants and density. P-waves (primary waves) are longitudinal waves where particle motion is parallel to the propagation direction, while S-waves (secondary waves) are transverse waves with perpendicular particle motion.
$$c_P = \sqrt{\frac{E(1-\nu)}{\rho(1+\nu)(1-2\nu)}}, \quad c_S = \sqrt{\frac{E}{2\rho(1+\nu)}} = \sqrt{\frac{G}{\rho}}$$
The velocity ratio $c_P/c_S = \sqrt{2(1-\nu)/(1-2\nu)}$ depends only on Poisson's ratio, regardless of material (approx. 1.73 for steel). The acoustic impedance $Z = \rho \cdot c_P$ is essential for reflection coefficient calculations in ultrasonic testing.
Wave equation: $\partial^2 u/\partial t^2 = c^2 \partial^2 u/\partial x^2$, with solution $u(x,t) = A\sin(kx - \omega t)$ ($k = \omega/c$).