The equation of wave is given by $\mathrm{Y}={10}^{-2}\sin 2\mathrm{\pi }(160\mathrm{t}-0.5\mathrm{x}+\mathrm{\pi }/4)$ , Where x and y are in m and t in s. The speed of the wave is …..  $\mathrm{km}{\mathrm{h}}^{-1}$

In the wave equation  $\mathrm{y}=\mathrm{Asin}(\mathrm{\omega t}-\mathrm{kx}+\mathrm{\varphi })$ 

Speed of wave, $\mathrm{v}=\frac{\mathrm{\omega }}{\mathrm{k}}$
Comparing given equation,
$\mathrm{\omega }{=}^{ }2\mathrm{\pi }\left(160\right),$

$\mathrm{K}=(0.5)2\mathrm{\pi }$

$\mathrm{v}=\frac{160}{0.5}=3200 \mathrm{m}/\mathrm{s}=320\times \frac{18}{5}\frac{\mathrm{km}}{\mathrm{hr}}=1152 \mathrm{km}/\mathrm{hr}$