My thanks to Peter Finch from St Joseph's College, Gregory Terrace, for these (pdf) solutions.
The rest are by Greg Rapkins:
In general: L = nl/4, where n = 1, 2, 3, 4, 5, .......
Points A, B, C, are points on the spring and therefore are moving outwards or inwards.
When the wave has gone 1 m further on point A is the same distance form the equilibrium.
Point B will have moved up to about the position o the 18 cm mark - a change of 38 cm.
Point c has moved soen to the -40 cm mark - a change of about -20 cm .
Therefore B has moved the greatest distance in the same time and therefore has the greatest velocity.
The velocity of the wave is 5 m s-1 and therefore goes 1 m in 0.2 of a second. When the wave has gone 1 m, C has moved down 20 cm.
Speed = distance / time = 20 cm/0.2 s = 100 cm s-1 = 1 m s-1.