As mentioned in the resource lesson on waves and vibrations, when we examine waves, information is usually displayed in two types of graphs, vibration graphs and waveform graphs. The shapes of both types of graphs are the same, the only difference is in the labels for the xaxis.
Vibration graphs display the behavior of a particle at a SINGLE location along the wave's path as time passes. One vibration can be defined as one complete cycle, or back and forth motion. On the following graph, as the disturbance passes point A in the medium, the first trough arrives at approximately 2.4 seconds and the last trough comes approximately 6.3 seconds later at 8.7 seconds.
Waveform graphs display the behavior of a multitude of locations at a SINGLE moment in time. At 3.1 seconds, the following graph shows that point A is located at an equilibrium position that is approximately 9.5 meters from the vantage point of the person documenting this wave.
Notice that these graphs depict different information about the periodic waves (sinusoidal) they illustrate.

vibration graphs

waveform graphs

shape

x

x

amplitude

x

x

wavelength


x

period

x


As shown in the previous chart, vibration graphs inform the reader of the wave's shape, amplitude, and period; while waveform graphs inform the reader of the wave's shape, amplitude, and wavelength.

The shape of a periodic wave is sinusoidal (based on either a sine or cosine graph).

The amplitude, A, is the wave's maximum disturbance from it undisturbed equilibrium position and represents the energy being transferred by the wave. Generally, the energy of a mechanical wave is proportional to the square of the wave's amplitude; i.e., if a wave's amplitude triples, its energy content is 9 times greater.

On a waveform graph, the wavelength, λ, is the distance between two adjacent inphase points on a waveform graph. A crest is a point of maximum positive amplitude along the wave while a trough is point of maximum negative amplitude.

On a vibration graph, the period, T, is the time between two adjacent inphase points on a vibration graph. The reciprocal of period is frequency, f. It represents the numbers of waves that pass a given location each second along the wave's path.
Although neither graph alone can answer the question of how fast the disturbance is traveling through the medium or in which direction it is moving, both of these questions can be answered when the graphs are used together. 