Problem $1($Pair Presentation$).$ The water surface elevation of a forward$-$propagating linear wave is given by:

$(x,t)=\frac{H}{2}cos(kx-t)$

Assume a wave height $H$ of $4m,$ a period $T$ of $10sec,$ and a wavelength $L$ of $100m.$

a$)$ Make a figure that shows that this equation produces a wave that moves to the right $($in the $+x$ direction$)$ as time advances $($similar to the figure in Lecture $01).$

Do this by making a graph of $($y$-$axis$)$ vs $x($x$-$axis$)$ from $-LxL($use $2$ meter increments on $x).$ Show the water surface at times of $t=0,2,$ and $4sec.$ Plot all $3$ curves on the same figure and label the axes and curves $($e$.$g$.,$ using a legend$)$ appropriately using the correct units.