A travelling wave is described by the equation $$y(x, t) = 0.05 \sin(8x - 4t)$$ m. The velocity of the wave is: [All the quantities are in SI unit]

Since the wave function is $$y(x,t) = 0.05\sin(8x - 4t)$$ m, we compare it with the general form of a travelling wave $$y = A\sin(kx - \omega t)$$, where the wave number is $$k$$ and the angular frequency is $$\omega$$; this reveals $$k = 8$$ rad/m, $$\omega = 4$$ rad/s, and the amplitude $$A = 0.05$$ m.

Therefore, the phase velocity is $$v = \frac{\omega}{k} = \frac{4}{8} = 0.5\;\text{m/s}$$, making the correct answer Option 3: 0.5 m s$$^{-1}$$.