A transverse wave on a string can be modeled by the equation

y$($x$,$ t$)=0\mathrm{.}364$ sin$(1\mathrm{.}30$x $+91\mathrm{.}0$t$),$

where x and y are in meters and t is in seconds. Imagine the string has a small mark on it at

x $=0.$

$($a$)$

What is the time interval $($in ms$)$ between the first two instants when this mark has a position of

y $=0\mathrm{.}175$ m$?$

ms

$($b$)$

What distance $($in m$)$ does the wave travel during the time interval found in part $($a$)?$

m