Speed and direction of a travelling wave

[sarvensogo]

Homework Statement

$$\Psi(y,t)=A\cos^22\pi(t-y)$$
Show that this is a traveling wave. Use the general form of a traveling wave to determine its speed and direction.
Verify your answer using $$\frac{-\partial \Psi / \partial t}{\partial \Psi / \partial x}$$

Homework Equations

The general form of a traveling wave from class is $$\Psi(x,t)=f(x-vt)$$.

The Attempt at a Solution

So I tried to just use the form of the traveling wave, but the thing that confused me was whether or not I had to switch around the order of (t-y) in the equation to (-y+t)? If I leave it as is I get that the speed (v) is -1, but if I change the equation to read (-y+t) the speed becomes 1 instead. Either way using the partial derivative equation verifies my answer. I can post my handwritten work if neccesary for proof that I attempted it.

Thanks

 

[mfb]

So I tried to just use the form of the traveling wave, but the thing that confused me was whether or not I had to switch around the order of (t-y) in the equation to (-y+t)? If I leave it as is I get that the speed (v) is -1, but if I change the equation to read (-y+t) the speed becomes 1 instead.

Please show your work (ideally typed here, that is easier to read. You can also use LaTeX). That should not happen as t-y is exactly the same as -y+t.