The given wave equation is $y(x,t) = 8.0\sin(0.5\pi x - 4\pi t - \frac{\pi}{4})$. Comparing this with the standard travelling wave equation $y(x,t) = A\sin(kx - \omega t + \phi)$, we get: Angular wave number, $k = 0.5\pi \text{ rad/m}$ Angular frequency, $\omega = 4\pi \text{ rad/s}$ The speed of the wave $v$ is given by the formula: $v = \frac{\omega}{k}$ $v = \frac{4\pi}{0.5\pi} = 8 \text{ m/s}$.