A sinusoidal sound wave moves through a medium and is described by the displacement wave function

s$($x$,$ t$)=2\mathrm{.}08$ cos$(15\mathrm{.}1$x $853$t$)$

where s is in micrometers, x is in meters, and t is in seconds.

$($a$)$ Find the amplitude of this wave.

$$m

$($b$)$ Find the wavelength of this wave.

cm

$($c$)$ Find the speed of this wave.

m$/$s

$($d$)$ Determine the instantaneous displacement from equilibrium of the elements of the medium at the position x $=0\mathrm{.}0494$ m at t $=2\mathrm{.}99$ ms$.$

$$m

$($e$)$ Determine the maximum speed of a element's oscillatory motion.

mm$/$s