A standing wave pattern on a string is described by

y$($x$,$ f$)=0\mathrm{.}040($sin $5$ mx$)($cos $40$ mt$),$

where x and y are in meters and r is in seconds. For x $0,$ what is the location of the node with the $($a$)$ smallest, $($b$)$ second small$-$est, and $($c$)$ third smallest value of x$?($d$)$ What is the period of the oscillatory motion of any $($nonnode$)$ point? What are the $($e$)$ speed and $($f$)$ amplitude of the two traveling waves that interfere to produce this wave? For t $0,$ what are the $($g$)$ first, $($h$)$ second, and $($i$)$ third time that all points on the string have zero transverse velocity?