Question

The displacement of an oscillator is written as
y(t) = a sin (ωt ± φ)
whereas the equation of a wave is written as
y(x, t) = a sin (ωt − kx)
Highlight the differences between the two.

Answer 1

The first dependence describes the displacement of the oscillator which as we see moves along y-axis and depends on time only.

The second function depends not only on time, but on the position of the considered point x also and describes a transverse wave.

The first equation includes a phase shift whereas the second doesn't.

The second equation allows defining velocity of the wave:

$$v=\frac{\omega}{k}.$$