9.1.2 Graphical Representation of Waves

Two types of graphs are commonly used to depict waves:

  1. Displacement-position graph: which shows a “snap-shot” of the entire wave profile at one particular instant in time.
  2. 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

a)

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.

b)

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.

Video Explanation

Is the particle going up or down?

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