A standing wave on a string is described by the equation

y$($x$,$ t$)=1\mathrm{.}32$ sin$(0\mathrm{.}0360$x$)$ cos$(1440$t$),$

where x is in centimeters, t is in seconds, and the resulting amplitude is in millimeters.

$($a$)$ What is the length of the string if this standing wave represents the first harmonic vibration of the string?

$($b$)$ What is the speed of the wave on this string?