Representing Waves on Graphs (Edexcel International A Level Physics)

Graphs of Transverse & Longitudinal Waves

Graphs of Transverse Waves

• There are two common graphs transverse waves;

  • Displacement against distance

  • Displacement against time

• These are:

  • Similar because they produce a sinusoidal shaped curve

  • Different because displacement against distance is showing displacement of a point on the wave, but displacement against time is showing the wave itself moving along a line

• On the displacement-distance graph:

  • Movement upwards from the centre line is given a positive sign and movement downwards a negative

  • The amplitude and wavelength can be found as shown below

• On the displacement-time graph:

  • The time period can be taken directly as shown

  • This means that frequency can be found indirectly as f = 1/T

• To determine the next position of a point on the wave

  • Sketch the full wave after time has passed by looking at the direction of travel

  • Each point oscillates perpendicular to the wave, so remains on the normal line wherever the wave intersects, this is shown in red below

Graphs of Longitudinal Waves

• Plotting displacement against distance also produces a sinusoidal shaped graph

  • This can be used to show where the compressions and rarefactions will be found

Graphs of Stationary Waves

• Stationary waves occur when a wave is reflected with a 180^o phase difference, creating a wave with a series of nodes and antinodes

  • Stationary waves can be transverse or longitudinal

  • They are represented graphically in the same way as progressive (travelling) waves

• Graphs of standing waves can also be used to determine the position of nodes and antinodes

• L is the length of the string

• 1 wavelength λ is only a portion of the length of the string