One end of a long string of linear mass density $8.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$ is connected to an electrically driven tuning fork of frequency $256 \mathrm{~Hz}$. The other end passes over a pulley and is tied to a pan containing a mass of $90 \mathrm{~kg}$. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At $t=0$, the left end (fork end) of the string $x=0$ has zero transverse displacement $(y=0)$ and is moving along positive $y$-direction. The amplitude of the wave is $5.0 \mathrm{~cm}$. Write down the transverse displacement y as a function of $x$ and $t$ that describes the wave on the string.