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

The wave equation is given as:

$$Y = 10^{-2}\sin 2\pi\left(160t - 0.5x + \frac{\pi}{4}\right)$$

Comparing with the standard form $$Y = A\sin(2\pi ft - 2\pi x/\lambda + \phi)$$:

$$2\pi f = 2\pi \times 160$$, so $$f = 160$$ Hz

$$\frac{2\pi}{\lambda} = 2\pi \times 0.5$$, so $$\frac{1}{\lambda} = 0.5$$ and $$\lambda = 2$$ m

Speed of the wave:

$$v = f\lambda = 160 \times 2 = 320 \text{ m/s}$$

Converting to km/h:

$$v = 320 \times \frac{3600}{1000} = 1152 \text{ km/h}$$

The speed of the wave is $$1152$$ km h$$^{-1}$$.