Linear mass density of the string is given as $\mu=8.0 \times 10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$
Frequency of the tuning fork is given as $=256 \mathrm{~Hz}$
Mass on the pan is given as $90 \mathrm{~kg}$
Tension on the string will be, $T=90 \times 9.8=882 \mathrm{~N}$
Amplitude is given as $A=0.05 \mathrm{~m}$
For a transverse wave, the velocity can be calculated as,
$v=\sqrt{\frac{T}{\mu}}=\sqrt{\frac{882}{8 \times 10^{-3}}}$
$=332 \mathrm{~m} / \mathrm{s}$
Angular frequency, $\omega=2 \pi \mathrm{f}$
$=2 \times 3.14 \times 256=1608.5 \mathrm{rad} / \mathrm{sec}$
Wavelength will be $\lambda=\mathrm{v} / \mathrm{f}=332 / 256=1.296 \mathrm{~m}$
Propagation constant will be $\mathrm{k}=2 \pi / \lambda=(2 \times 3.14) / 1.296$
$=4.845 \mathrm{~m}^{-1}$
The general equation of the wave is
$y(x, t)=A \sin (\omega t-k x)$
On Substituting all the values we get
$y(x, t)=A \sin (1608.5 t-4.845 x)$
$x$ and $y$ are in metre and $t$ is in seconds.