Find the Speed and Direction of a Wave with Constants A, B, and C

[azatkgz]

Homework Statement

What's the speed and direction of the following wave(A,B and C are constants)
$$y(x,t)=Ae^{Bx^2+BC^2t^2-2BCxt}$$

The Attempt at a Solution

$$y(x,t)=Ae^{B(x-Ct)^2}$$

from (x-Ct)

v=C in the +x direction

 

[Mindscrape]

Are you missing the imaginary constant in your exponential? If so, then you are correct. If not, you have a diverging or decaying exponential rather than a plane wave.

 

[azatkgz]

No,it's original question.There's no imaginary constant.
So my solution is true.Thanks for checking.

 

[Mindscrape]

No, there has to be an imaginary constant. You need to have something of the form

$$Ae^{i(x-vt)}$$

Regular exponentials don't satisfy the wave equation. The wave equation says that two derivatives in time equal two derivatives in space divided by the velocity squared.