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4.6.4Electrons, Waves and Photons

Graphical Representations of Transverse and Longitudinal Waves — OCR A Level Physics A H556 Revision Notes & Topical Questions

5 min read 5 parts Lesson 45 of 62 Unit quiz

📚 OCR A Level Physics A H556 Hub / Topical Revision
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Curriculum Equation Key Wave Speed & Doppler Effect FormulasFast Exam Solution
v = f × λ | f_obs = f × (v ± v_o) / (v ∓ v_s) | T = 1 / f
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Part 1 of 5Two Types of Graph

4.6.4 Graphical Representations of Transverse and Longitudinal Waves

The same wave can be plotted against distance or against time, and the two graphs reveal different quantities.

Displacement-distance
  • This graph is a snapshot of all points along the wave at one instant; its repeat distance is the wavelength.
Displacement-time
  • This graph follows one point as time passes; its repeat time is the period.
Amplitude
  • On both graphs the amplitude is the maximum height of the curve above the equilibrium (zero) line.
Shape
  • A single-frequency wave gives a sinusoidal curve in either graph.

Part 2 of 5Longitudinal Waves on a Graph

Longitudinal Waves on a Graph
Displacement meaning
  • Positive displacement means a particle has moved in the direction of wave travel and negative means the opposite direction.
Graph shape
  • Plotting displacement against distance gives the same sinusoidal curve as for a transverse wave.
Compressions
  • Compressions occur where neighbouring particles are displaced towards each other, not at the peaks of the graph.
Rarefactions
  • Rarefactions occur where neighbouring particles move apart, so the particles are spread widest there.

Part 3 of 5Reading the Graphs

1
Read the amplitude as the vertical distance from the zero line to a peak, remembering the units on the axis.
2
Read the wavelength from the horizontal distance between two successive peaks on the displacement-distance graph.
3
Read the period from the horizontal time between two successive peaks on the displacement-time graph.
4
Calculate the frequency from f = 1/T and then the wave speed from v = fλ.
5
Combine data from both graphs only when they describe the same wave.

Part 4 of 5Worked Example

Question

  • A displacement-time graph shows 4 complete cycles in 0.020 s.
  • A displacement-distance graph of the same wave has a wavelength of 0.50 m.
  • Find the frequency and wave speed.

  1. Period T = 0.020 / 4 = 0.0050 s.
  2. Frequency f = 1/T = 1 / 0.0050 = 200 Hz.
  3. Wave speed v = fλ = 200 × 0.50 = 100 m s⁻¹.

Answer f = 200 Hz and v = 100 m s⁻¹.

Part 5 of 5Exam Checklist & Tips

4.6.4 – Key Points for the Exam

  • Displacement-distance graph A graph of displacement against position along the wave at one instant.
  • Displacement-time graph A graph of displacement of one point against time.
  • Equilibrium position The position of a particle when no wave is present.
  • Sinusoidal Having the smooth repeating shape of a sine or cosine curve.

Common Mistakes

  • Reading wavelength from a displacement-time graph, where the repeat is the period.
  • Assuming the peak of a longitudinal graph is a compression.
  • Measuring amplitude from peak to trough instead of from the equilibrium line.
  • Using the wrong graph to calculate frequency.

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