Graphs of Waves

Displacement-Distance Graph

The displacement-distance graph shows the displacement of particles in the medium at a specific moment in time as a function of their position along the wave's direction of travel. This graph gives a snapshot of the wave's shape at that instant.

The physical quantities that can be directly obtained from the displacement-distance graph are its amplitude and wavelength.

The amplitude, A, is the maximum displacement of particles from their rest position.
📖 The wavelength, λ, is the distance between two consecutive points in phase, such as between two adjacent crests.
100 mm

Displacement-Time Graph

The displacement-time graph shows the displacement of a particular particle in the medium as a function of time. This graph gives insight into how the displacement of a single point on the wave varies over time.

The physical quantities that can be directly obtained from the displacement-distance graph are its amplitude and period.

The period, T, is the time taken for one complete cycle of the wave.

From the period, we can also calculate the frequency f using the equation $$f =\dfrac{1}{T}$$

📖 The frequency, f, is the number of wave cycles per second.

The SI unit of frequency is the hertz (Hz) and is equivalent to s-1.

In the graph below, you can adjust the frequency to observe the change in the period and number of waves produced over the given time.

10 Hz

A Moving Displacement-Distance Graph

Since the displacement-distance graph is a snapshot of the wave's shape at that instant, the waveform will move over time. This is illustrated using the interactive below. You can choose to have the wave move either towards the left or the right. Observe what happens to the position of the chosen particle. It does not move along with the direction of wave motion or energy transfer, but vertically along the same line and remains as part of the waveform.