5.5 Representing Waves on Graphs

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

ANSWER:   A

• 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