For a travelling harmonic wave y(x, t) = 2.0\ \ 2π(10\ t - 0.0080\...

The given equation of the travelling harmonic wave is $y(x, t) = 2.0 \cos 2\pi(10 t - 0.0080 x + 0.35)$.

Comparing this with the standard wave equation $y(x, t) = A \cos(\omega t - kx + \phi_0)$, we get the wave number $k = 2\pi \times 0.0080$ rad/cm.

The distance between the two points is given as $\Delta x = 0.5$ m $= 50$ cm.

The phase difference $\Delta \phi$ between two points separated by a distance $\Delta x$ is given by $\Delta \phi = k \Delta x$.

Substituting the values, we get:

$\Delta \phi = (2\pi \times 0.0080) \times 50$

$\Delta \phi = 2\pi \times 0.4 = 0.8\pi$ rad.

Answer: $0.8\ \pi$ rad