The string shown in the figure is driven at a frequency of $5\mathrm{.}00Hz.$ The amplitude of the motion is $A=14\mathrm{.}5cm,$ and the wave speed is $v=17\mathrm{.}5\frac{m}{s}.$ 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$).$

$ra\frac{d}{s}$

$($b$)$ Determine the wave number for this wave $($in $ra\frac{d}{m}).$

$ra\frac{d}{m}$

$($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 $\frac{m}{s}).$

$\frac{m}{s}$

$($e$)$ Calculate the maximum transverse acceleration of an element of the string $($in $\frac{m}{s^2}).$

$\frac{m}{s^2}$

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

maximum transverse speed

$\frac{m}{s}$

maximum transverse acceleration

$\frac{m}{s^2}$