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4.9.2Electrons, Waves and Photons

Graphical Representation of Superposition — OCR A Level Physics A H556 Revision Notes & Topical Questions

5 min read 5 parts Lesson 55 of 62 Unit quiz

📚 OCR A Level Physics A H556 Hub / Topical Revision
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Part 1 of 5Point-by-Point Addition

4.9.2 Graphical Representation of Superposition

Because displacements simply add, the resultant can be drawn without any complicated calculation.

1
Draw the two waves on the same axes with identical scales for displacement and for position or time.
2
Choose a series of positions along the horizontal axis, such as peaks, troughs and zero crossings.
3
At each chosen position, read both displacements and add them, keeping their signs.
4
Plot the sum at that position and repeat for enough positions to see the shape.
5
Join the plotted points with a smooth curve to show the resultant wave.

Part 2 of 5Special Cases

In phase
  • When two equal waves line up crest to crest, the resultant has an amplitude equal to the sum of the amplitudes.
Antiphase
  • When one wave's crest meets another's trough, the displacements cancel and equal amplitudes give zero.
Unequal amplitudes
  • In antiphase with different amplitudes, the resultant has amplitude equal to the difference.
Phase difference
  • A phase difference of 180°, or π rad, means half a cycle apart, giving the antiphase condition.
Phase differenceNameResultant amplitude (equal waves)
0° (0)In phaseDoubled
180° (π)AntiphaseZero

Part 3 of 5Reading the Graphs

Reading the Graphs
Frequency
  • If the two waves have the same frequency, the resultant has that frequency too.
Amplitude check
  • The resultant's amplitude always lies between the difference and the sum of the two amplitudes.
Zero crossing
  • Where both waves cross zero together, the resultant is also zero.
Different frequencies
  • Waves of different frequencies produce a resultant with a changing amplitude pattern.

Part 4 of 5Worked Example

Question

  • Two waves of the same frequency have amplitudes 4.0 mm and 2.5 mm.
  • State the amplitude of the resultant when they are in phase and when they are in antiphase.

  1. In phaseamplitudes add, 4.0 + 2.5 = 6.5 mm.
  2. In antiphaseamplitudes subtract, 4.0 − 2.5 = 1.5 mm.

Answer 6.5 mm in phase and 1.5 mm in antiphase.

Part 5 of 5Exam Checklist & Tips

4.9.2 – Key Points for the Exam

  • Phase difference How far one wave is ahead of another, measured in degrees or radians.
  • In phase Having a phase difference of zero, so crests coincide.
  • Antiphase Having a phase difference of 180° so crest meets trough.
  • Resultant wave The wave produced by adding the waves present at each point.

Common Mistakes

  • Adding the wave heights without paying attention to the signs of the displacements.
  • Assuming antiphase waves of unequal amplitude cancel exactly.
  • Plotting too few points, which gives a misleading shape.
  • Using different scales for the two waves.

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