9.1.2 Graphical Representation of Waves

Two types of graphs are commonly used to depict waves:

Displacement-position graph: which shows a “snap-shot” of the entire wave profile at one particular instant in time.
Displacement-time graph: which shows the oscillation of one particular point on the wave.

Example 1

If the displacement-position graph below is for a rightward traveling wave at $\displaystyle t=0$ , sketch the displacement-time graphs for the oscillations at position A and B.

Solution

Example 2

Deduce the direction of motion at A, if the graph is

a) a displacement-position graph of a wave traveling rightward.

b) a displacement-time graph.

Assume that positive displacement is upward, and negative displacement is downward.

Solution

Since this is a displacement-position graph, A is a particular point on the wave. By mentally “animating” the wave profile rightward, we can deduce that point A is having a downward motion at this instant in time.

Since this is a displacement-position graph, A is a particular instant in time. At this instant, the oscillation’s displacement is positive and becoming more positive. So the oscillation is having an upward motion at the instant A.