(4-3)  The picture below shows snapshots of two waves, taken after increasing periods of time (t):

①  Taking first the wave shown in blue. Find its amplitude, velocity and wavelength. Also note the value of y when x and t are both 0. (Do not worry about units – just treat everything as a number here).

②  Hence write down the equation for this wave as a function of the form y = f(x,t).

③  Now look at the wave shown in orange. You can see that it has the same amplitude, wavelength and velocity as the blue wave. The only difference is that it is shifted to the left compared to the blue one. This is similar to case (d) in Question 4-1 but the waves are relatively shifted by ⅝ in the present case. See if you can therefore write down the equation for the orange wave.

④  Hence write down a general equation for a travelling sinusoidal wave, having now removed the stipulation that y=0 when x and t are 0.