Please write down the general wave equation in fluid and solid. Show the simple solution of the wave equations, and discuss the wave velocities. Define all the parameters you need for the equations. Solution For fluids,\\(\\frac{\\partial P}{\\partial t}+\\frac{\\partial (\ ho u_{x})}{\\partial x}+\\frac{\\partial (\ ho u_{y})}{\\partial y}+\\frac{\\partial (\ ho u_{z})}{\\partial z}=0\\) P=Pressure rho=density ux=velocity in x direction and so on. For solids, \\(\\frac{\\partial^{2}\\xi}{\\partial x^{2}}-\\frac{\ ho}{E}*\\frac{\\partial^{2}\\xi}{\\partial t^{2}}+\\frac{q}{E}=0\\) \\xi=stress x=x direction t=time rho=density E=young\'s modulus q=external forces/unit volume..

1. Please write down the general wave equation in fluid and solid. Show the simple solution of the
wave equations, and discuss the wave velocities. Define all the parameters you need for the
equations.
Solution
For fluids,(frac{partial P}{partial t}+frac{partial ( ho u_{x})}{partial
x}+frac{partial ( ho u_{y})}{partial y}+frac{partial ( ho u_{z})}{partial z}=0)
P=Pressure
rho=density
ux=velocity in x direction and so on.
For solids,
(frac{partial^{2}xi}{partial x^{2}}-frac{ ho}{E}*frac{partial^{2}xi}{partial
t^{2}}+frac{q}{E}=0)
xi=stress
x=x direction
t=time
rho=density
E=young's modulus
q=external forces/unit volume.