suppose a string has a wave move through it with the following function: y$($x$,$ t$)=2\mathrm{.}4$ cos$(3$t $+1\mathrm{.}1$x$),$

where all appropriate units are assumed. $($i$)$ If the maximum speed of a particle on the string was

the speed of sound in an open$-$open pipe that had a fundamental frequency of $1200$ Hz$,$ determine the

length of the pipe. $($ii$)$ Prove the function satisfies the linear wave equation.