Waves: basic terms & graphical representation

Some basic ideas about waves can be demonstrated using mechanical waves along strings or springs, ripples on water, or special wave machines. The system carrying the waves is called the medium. A displacement against distance graph, or wave profile, shows the displacement of points along the medium at one instant of time.

In the figure above, waves on the spring are being started by oscillations of the end P1. At the instant shown, P1 has completed two oscillations. All other points along the medium perform the same oscillations as P1, only later in time. P5 is just starting to oscillate; P3 has performed one complete oscillation; P2 and P4 are also oscillating, half a cycle (p) out of phase with P1. The distance between any two adjacent points which are in phase is one wavelength (l).

Another graph, of displacement against time, could be plotted for any particular point along the medium. From this graph the period , T , and frequency , f , could be obtained. The figure below shows a displacement against time graph for the point P5, assuming that the wave profile above represents displacements at t = 0.

The speed of travel of the wave, c , is given by c = f × λ. If P1 oscillates continuously, a continuous wave travels along the spring. If, however, P1 is just displaced once and then remains at its equilibrium position, a single pulse travels along the spring.