The string shown in the figure is driven at a frequency of $5\mathrm{.}00$ Hz$.$ The amplitude of the motion is A $=11\mathrm{.}5$ cm$,$ and the wave speed is v $=21\mathrm{.}0$m$/$s$.$

Furthermore, the wave is such that y $=0$ at x $=0$ and t $=0.$

$($a$)$Determine the angular frequency for this wave $($in rad$/$s$).$

$($b$)$Determine the wave number for this wave $($in rad$/$m$).$

$($c$)$Write an expression for the wave function. $($Use the following as necessary: t$,$ x$.$ Let x be in meters and t be in seconds. Do not include units in your answer. Assume SI units.$)$

y $=$ sin $()$

$($d$)$Calculate the maximum transverse speed $($in m$/$s$).$

$($e$)$Calculate the maximum transverse acceleration of an element of the string $($in m$/$s$2).$

$($f$)$What If$?$ If the driving frequency is now doubled to $10\mathrm{.}0$ Hz$,$ what are the maximum transverse speed $($in m$/$s$)$ and maximum transverse acceleration $($in m$/$s$2)$ of an element of the string?

maximum transverse speed m$/$smaximum transverse acceleration