A sinusoidal wave is sent along a string with a linear density of $\backslash (2\mathrm{.}25\backslash$mathrm$\{$~g$\}/\backslash$mathrm$\{$m$\}\backslash ).$ As it travels, the kinetic energies of the mass elements along the string vary. Figure $($a$)$ gives the rate $\backslash ($ d K $/$ d t $\backslash )$ at which kinetic energy passes through the string elements at a particular instant, plotted as a function of distance $\backslash ($ x $\backslash )$ along the string. Figure $($b$)$ is similar except that it gives the rate at which kinetic energy passes through a particular mass element $($at a particular location$),$ plotted as a function of time $\backslash ($ t $\backslash ).$ For both figures, the scale on the vertical $($rate$)$ axis is set by $\backslash ($ R$\_\{$s$\}=13\backslash$mathrm$\{$~W$\}\backslash ).$ What is the amplitude of the wave?

$($a$)$