A transverse sinusoidal wave is moving along a string in the positive direction of an x axis with a speed of $83$ m$/$s$.$ At t $=0,$ the string

particle at x $=$ O has a transverse displacement of $4\mathrm{.}0$ cm from its equilibrium position and is not moving. The maximum transverse

speed of the string particle at x $=0$ is $20$ m$/$s$.($a$)$ What is the frequency of the wave? $($b$)$ What is the wavelength of the wave? If the

wave equation is of the form y$($x$,$ t$)=$ Ym sin$($kx $$ wt $+),$ what are $($c$)$ Ym$,($d$)$ k$,($e$)$ w$,($f$),$ and $($g$)$ the correct choice of sign in front of w$?$