Solution

1)If the two particles are separated by a distance λ, they will differ by a phase of 2π. Therefore, the phase φ of the particle P at a distance

x is φ = (2π/λ) x

y = a sin (ωt - 2πx/λ)

Progressive wave will have t and x variables in a function that is defined for all x.

2) Stationary wave fixed at both ends will have nodes at both ends. The nodes in between the ends vary as per the wavelength of the wave and hence not well defined.

3) Visible.light is an Electromagnetic wave with very high frequencies (in the range of 10^14Hz) hence observing beats is not possible.