1. The problem statement, all variables and given/known data psi(x,y)= Asin((ax^2)-(by^2)) Does this expression represent a traveling wave? If so what is the direction and speed of the wave? 2. Relevant equations This wave resembles a a harmonic wave. psi(x,t)= Asin(kx-wt+phi) 3. The attempt at a solution Ok, A,a,b are constants. I do not think this expression represents a traveling wave because the argument of the sin function is to the second order. For an expression to represent a traveling wave does the expression have to be to the first order, or only a certain part of the expression. 1. sin(x+y)^2 2. sin^2(x+y) does these represent traveling waves? 1 has the argument squared. if we multiply out the argument is no longer linear, and thus not a traveling wave? 2 has the entire function squared, is this a traveling wave? What are some characteristics of traveling waves, mathematically? Thank you.