$34...$ A transverse wave on a string has an amplitude of $20$ cm$,$ a wavelength of $35$ cm$,$ and a frequency of $2\mathrm{.}0$ Hz$.$ Write the mathematical description of the displacement from equilibrium for the wave if $($a$)$ at t $=0,$ x $=0$ and y $=0$; $($b$)$ at t $=0,$ x$=0$ and y $=+20$ cm; $($c$)$ at t $=0,$ x $=0$ and y $=-20$ cm; and $($d$)$ at t $=0,$ x $=0$ and y $=12$ cm$.$ Example $13-2$