How can i tell if an expression represents a traveling wave?

[sigmint]

Homework Statement

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?

Homework Equations

This wave resembles a a harmonic wave.

psi(x,t)= Asin(kx-wt+phi)

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.

 

[Antenna Guy]

Homework Equations

This wave resembles a a harmonic wave.

psi(x,t)= Asin(kx-wt+phi)


What are some characteristics of traveling waves, mathematically?

$kx-\omega t=0$

$(kx)^2-(\omega t)^2=0$ too.

$$k=\frac{2\pi}{\lambda}$$

$$\lambda=\frac{v}{f}=\frac{2\pi}{k}$$

$$f=\frac{\omega}{2\pi}$$

You can solve for v in terms of a and b using the above, but it assumes that y is analogous to t.

Regards,

Bill