# Power in Wave Motion

As we know Power for transverse wave is P=(Fu)1/2 x A2w2 Sin2(kx-wt) for the wave traveling in +x direction represented by Y=ACos(kx - wt) . However for wave traveling in -x direction is P= -(Fu)1/2 x A2w2 Sin2(Kx-wt) . (Note the negative sign)

The Problem is I am not able to derive this. In derivation I am not getting the negative sign (which i suppose to). Could someone please explain what is power in transverse wave traveling to left represented by Y=ACos(kx + wt).

The concept I am applying is Instantaneous power P=F.V. Please see the diagram.

I hope you can understand what i am saying