Parameter

Equations

Definitions

v_s and v_p wave velocity

$v=\frac{x}{t}$ (m/s)

x: Marble thickness

t: Duration of passage

µ Lame constant

$v_s=\sqrt{\frac{\mu }{\rho }}$ (m/s)

v_s: Transverse wave velocity

ρ: Marble density

λ Lame constant

$v_p=\sqrt{\frac{\lambda +2\mu }{\rho }}$ (m/s)

v_p: Longitudinal wave velocity

σ Poisson ratio

$\sigma =\frac{\lambda }{2\times \left(\lambda +\mu \right)}$

Y Young modulus

$Y=\frac{\mu \times \left(3\lambda +2\mu \right)}{\lambda +\mu }$ (N/m²)

B Volume modulus

$B=\lambda +2\mu$ (N/m²)

K Compression coefficient

$K=\frac{1}{B}$ (m²/N)

E Dynamic Elastic Constant

$E=\frac{\left(1+\sigma \right)\times \left(1-2\sigma \right)}{\left(1-\sigma \right)}\times v_p^2\times \frac{\rho }{g}\times {10}^5$ (kg/cm²)