(e) graphical representations of transverse and longitudinal waves

The idea

A displacement–distance graph shows the displacement of particles from their rest positions along the direction of travel at one instant; a displacement–time graph shows how the displacement of one particle varies with time. For a transverse wave, particle displacement is perpendicular to the direction of energy transfer, so the graph looks like a familiar sine curve. For a longitudinal wave, particle displacement is parallel to the direction of travel, producing compressions where particles bunch together and rarefactions where they spread apart. On a displacement–distance graph, one full cycle spans one wavelength λ; on a displacement–time graph, one full cycle spans one period T. Amplitude is the maximum displacement from the rest position on either graph.

What earns the marks

• Distinguishes displacement–distance graphs (snapshot of many particles at one time) from displacement–time graphs (history of one particle).
• Identifies amplitude as the maximum displacement from the rest position on either graph.
• Reads wavelength λ from one complete cycle on a displacement–distance graph and period T from one complete cycle on a displacement–time graph.
• Describes transverse waves as having displacement perpendicular to the direction of travel and longitudinal waves as having displacement parallel to it, with compressions and rarefactions.

Common mistakes and how to put them right

• Reading wavelength from a displacement–time graph.

  Put it right: A displacement–time graph gives the period T, while wavelength comes from a displacement–distance graph.

• Treating the vertical axis as distance travelled.

  Put it right: The vertical axis is displacement from the rest position, which can be positive or negative.

• Believing longitudinal waves cannot be represented graphically.

  Put it right: A displacement–distance graph can show compressions and rarefactions as regions of large displacement gradient.

Exam tips

• Label the axes with quantity and unit before reading values from a graph.
• Count complete cycles carefully: one cycle runs from one point to the next identical point in phase.
• For longitudinal waves, link compressions to regions where particles are closest together and rarefactions to regions where they are furthest apart.