Question

if E(x,t)=sin(2*pi*(at-x/3)) how do you determined the velocity of wave? thank you

Answer 1

Remember the units. Velocity is m/s. Frequency is 1/s and wavelength is m. All you need to do is extract the wavelength and frequency from that and use
\[v = \nu \lambda\]
where nu is the frequency and lambda is the wavelength. That equation is using radians. Recall that the wavenumber, k, goes with the spatial "x" part and is
\[k = 2 \pi / \lambda\]
the "a" in this case is the frequency. Recall angular frequency is
\[\omega = 2 \pi \nu\]

Answer 2

The vertical point of the graph E(x,t) is given by the horizontal position x and the time t. E(x,t) = sin(2*pi*(at-x/v) is the general form the equation. v is the velocity of the wave. In your question the velocity is given, 3.