Representing Waves on Graphs (Edexcel International AS Physics): Revision Note

Graphs of Transverse & Longitudinal Waves

Representing transverse waves

• Transverse waves are commonly represented using:

  • displacement-distance graphs

  • displacement-time graphs

• On the displacement-distance graph:

  • amplitude is measured from the rest position to the point of maximum displacement

  • wavelength is measured from one point on a wave to the same point on the next wave (e.g. two consecutive crests or troughs)

• On the displacement-time graph:

  • period is measured from one point on a wave to the same point on the next wave

  • frequency can be calculated using

Transverse waves can be graphed to visualise the perpendicular vibrations over distance or time

• 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 it remains on the normal line wherever the wave intersects, as shown in red below

Representing longitudinal waves

• Longitudinal waves can be represented using:

  • displacement-distance graphs

  • pressure-distance graphs

• On the displacement-distance graph:

  • the amplitude and wavelength can be measured in the same way as the transverse wave

  • zero displacement occurs at compressions and rarefactions

  • maximum displacement occurs halfway between compressions and rarefactions

• The pressure-distance graph is:

  • highest at compressions and lowest at rarefactions

  • 90° out of phase with the displacement graph

Longitudinal waves can be graphed to visualise the displacement of particles at different positions, as well as the pressure at each position

• A sound wave is a longitudinal wave caused by oscillations of particles in the medium, e.g. air molecules

• At a compression:

  • air molecules have zero displacement (compared to their equilibrium positions)

  • air molecules on either side are displaced towards it

  • this creates an area of high pressure

• At a rarefaction:

  • air molecules have zero displacement (compared to their equilibrium positions)

  • air molecules on either side are displaced away from it

  • this creates an area of low pressure

The positions of air molecules in a sound wave can be mapped onto a displacement-distance graph

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