Question

I've been given an equation that is of the form y=2Asin(kx)cos(wt). I need to identify the amplitude, freq., wavelength, speed, and direcgtion of the component waves that make up this wave of superposition... I'm not sure what all I have in this equation given...

Answer 1

amplitude= A/2
frequency=w/2pi
speed= w/k
wavelength=v/f
and the directions of the component waves=opposite directions... I believe due to Euler's Rule...not real sure on that one.
Yes I did answer my own question... I hadn't realized that I knew it! lol

Answer 2

To find the constituent waves, just do the reverse of what you did to get to this equation - expand it.
\[2Asin(kx)\cos(omegat)=A(2\sin(kx)\cos(omegat))\]
=\[A(\sin(kx+wt) + \sin(kx-wt))\]
=\[Asin(kx+wt)+Asin(kx-wt)\]
These two terms are your constituent waves. They clearly have amplitude A and travel in opposite directions