Somebody explain this year old why waves move the way they do and how can I imagine energy transfer?

PS:My First Thread.

Best thing you can do is get some rope/string and a slinky spring. Have a play with them and see what wave phenomena you can see.

 

In particular look for longitudinal and transverse wave motions, reflected waves and how waves interfere with each other.

This website may help as well, it has a number of simulations, and variables you can fiddle around with...

 

http://www.hazelwood.k12.mo.us/~grichert/sciweb/waves.htm

One of the ways you can write a solution to the (1-D scalar linear) wave equation is u(x,t) (the solution) = F(x-c*t) + G(x+ct) where c is the speed of the wave. The exact form of the functions F&G are based on the boundary and initial conditions. But, you can see how they behave from their form. At time t=0, you have F(x). At time t=(1/c), you have F(x-1), or to look at it in another way, the information from F(x) has now been transferred over to x-1. Exactly how a wave moves from one side to the other. In the same way, at time t=(1/c) the information that was at G(x) is now at G(x+1). Information moves both ways, depending on whether it is information on F or G. This is because the wave equation is linear, so the information that is formally seperated into F & G can be summed to get the final answer. Finally, what I wrote is just a discussion about the mathematics behind the wave equation, but there are many, many situations where the mathematical abstraction is an exceptionally good model for real physics. Any medium where dissipation is very low the wave equation will be applicable. Also, for fast time scales, the wave equation is good -- basically so long as the time you are modeling is short dissipation won't have time to take effect.