Question

Here are the equations of three waves:

(1) y(x, t) = 2 sin(4x − 2t),

(2) y(x, t) = sin(3x − 4t),

(3) y(x, t) = 2 sin(3x − 3t).

Rank the waves according to their (a) wave speed and (b) maximum transverse speed, greatest first.

Answer 1

I think that we have to compare your waves, with this more general plane wave:
\[\huge W\left( {{\mathbf{r}},t} \right) = {W_0}{e^{\frac{i}{\hbar }\left( {{\mathbf{p}} \cdot {\mathbf{r}} - Et} \right)}}\]

Answer 2

\(W_0 [\cos ((p\cdot r-Et)/h) + i\sin((p\cdot r-Et)/h)] \) ?

what do h, p and E represent here ?

I know \(v =\dfrac{\lambda}{T}\)

Answer 3

yes! here is the meaning s of \(\hbar \) and \(e\)
\(\hbar \) is the reduced Planck constant, whereas \(E\) is the energy of the particle represented by such wave

Answer 4

the phase speed is: \(v=\nu \; \lambda\), namely your expression above