Given the wave equation:

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

Comparing this equation with the general form:

$$Y = A \sin(2\pi(ft - kx + \phi))$$

We can identify the wave number $$k = 0.5\,\mathrm{m}^{-1}$$ and the frequency $$f = 160\,\mathrm{Hz}$$. The wave speed $$v$$ can be found using the relationship between wave number, wave speed, and frequency:

$$v = \frac{\omega}{k} = \frac{2\pi f}{2\pi k}$$

Now, we can calculate the wave speed:

$$v = \frac{2\pi \times 160}{2\pi \times 0.5} = \frac{160}{0.5}\,\mathrm{m/s}$$

$$v = 320\,\mathrm{m/s}$$

Now, we need to convert the wave speed from meters per second to kilometers per hour:

$$v = 320 \frac{\mathrm{m}}{\mathrm{s}} \times \frac{1\,\mathrm{km}}{1000\,\mathrm{m}} \times \frac{3600\,\mathrm{s}}{1\,\mathrm{h}}$$

$$v = 320 \times \frac{1}{1000} \times 3600\,\mathrm{km/h}$$

$$v = 1152\,\mathrm{km/h}$$

So, the speed of the wave is $$1152\,\mathrm{km/h}$$.