What is the meaning of the wave equation?

Question

anonymous · Answer

I am just starting to studying waves in physics and I recently learned how to derive the wave equation:$$\delta ^{2}y/\delta x^2=(1/v^2)(\delta^2y/\delta t^2)$$My trouble is, I have know idea what that means. Is it describing the motion of the wave, the speed of the wave, or what? I can't seem to find an answer and my textbook doesn't do a very good job explaining it. Any help would be appreciated. 

P.S. I know the notion is wrong. I could only use delta, here, but I know delta is not the correct notion for the partial derivative.

anonymous · Answer

The "displacement" y is a function both of distance, x, and time, t.

A traveling wave will have a shape that moves along the x axis at velocity v...that's how the peak will move, for example.

A standing wave will have fixed positions along x for its zeros (nodes) and maxima, but will oscillate up and down between these positions.

masumanwar · Answer

how the wave evolve in space like matter move for motion equation such as wave equation for wave

anonymous · Answer

Thanks!

anonymous · Answer

Glad we were of some help.