Theme C — Wave Behaviour
C.3.5 Superposition of Waves — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 21 of 37 1 quiz
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
Lesson summary
C.3.5 Superposition of Waves — IB PHYSICS SL notes: Apply the principle of superposition to find the resultant of two waves, including graphical addition, pulses, beats and coherence.Principle of superposition — when two or more waves overlap at a point, the resultant displacemen…
- Interference
- After overlap
- Constructive
- Destructive
- Equal waves
- Energy conservation
Part 1 of 8Principle of superposition
1Principle of superposition
- Principle of superposition when two or more waves overlap at a point, the resultant displacement is the sum of the individual displacements
- Displacements add as vectors, so signs matter.
- Displacements in the same direction add and those in opposite directions subtract.
2Interference
- Interference the effect of the overlap is called interference
3After overlap
- After overlap the waves continue unchanged, each with its original shape
- This is why several instruments in an orchestra can be heard separately.
- Ripples that cross a pond emerge unaffected by each other.
4Limit
- Limit it applies to waves that do not change the medium so strongly that its response becomes non-linear
Part 2 of 8Constructive and destructive superposition
Constructive
- Constructive waves in phase add to a larger amplitude
- (crest meets crest)
Destructive
- Destructive waves in antiphase partly or fully cancel
- (crest meets trough)
Equal waves
- Equal waves constructive superposition gives amplitude 2x0, and destructive superposition gives zero
Intensity
- Intensity it is proportional to amplitude squared, so two equal waves in phase give four times, not twice, the intensity of one
Energy conservation
- Energy conservation intensity is raised in some places and reduced in others, so the average equals the sum of the individual intensities
Part 3 of 8Adding waves graphically
1
Choose points along the horizontal axis.
2
At each point read the heights of the two curves, with signs.
3
Add the heights.
4
Plot the sums as a new curve.
1Identical waves in phase
- Identical waves in phase the sum has the same shape with doubled amplitude
2Identical waves in antiphase
- Identical waves in antiphase the sum is a straight line along the axis
3Both graph types
- Both graph types the method works on displacement–position and displacement–time graphs
Part 4 of 8Pulses
Opposite pulses
- Opposite pulses a crest and a trough travelling towards each other cancel momentarily in the middle, then emerge unchanged
- At complete cancellation the rope is flat but its energy is held as kinetic energy of the moving rope particles.
Equal pulses
- Equal pulses two crests momentarily give a double-height pulse
Result
- Result the resultant displacement is always the algebraic sum of the individual displacements
Part 5 of 8Beats
Beats
- Beats a periodic variation in amplitude when two waves of slightly different frequency add
- For sound it is an audible wobble in loudness.
Beat frequency
- Beat frequency fb = |f1 − f2|, the difference and not the average
Mathematical origin
- Mathematical origin two equal-amplitude sine waves of nearby frequencies form a fast oscillation inside a slowly varying envelope
Part 6 of 8Coherence
Coherent sources
- Coherent sources sources with the same frequency and wave type and a constant phase difference
Requirement
- Requirement a stable interference pattern needs coherent sources
Separate bulbs
- Separate bulbs they are not coherent, because their phases change randomly millions of times a second and the pattern averages to uniform brightness
Method
- Method split a single wave, for example by sending it through two slits
Part 7 of 8Everyday examples
Everyday examples
Soap bubbles and oil films
- Soap bubbles and oil films their colours come from interference of light reflected from the front and back surfaces
Car radio
- Car radio reception fades where direct and reflected signals cancel
Concert halls
- Concert halls surfaces are arranged so that reflected sound adds in the audience area without dead spots
Water ripples
- Water ripples dogs or sources making waves in water give areas of zero displacement and areas of raised displacement
Standing waves
- Standing waves superposition of waves travelling in opposite directions is the basis of standing waves
Part 8 of 8More from the specification
1Snell's Law and Refraction at Boundaries
- When light crosses a boundary into a medium of higher refractive index, wavefronts slow down and bend towards the normal,
- reducing wavelength while frequency remains unchanged.
- (n₁ sin θ₁ = n₂ sin θ₂)
2Refractive Index and Material Optical Density
- The absolute refractive index n is the ratio of wave speed in vacuum to speed in the material (n = c/v), determining the critical angle of incidence.What the symbols mean: n = refractive index (no unit) · c = speed of light in a vacuum (3.00 × 108 m s−1) · v = speed of light in the material (m s−1)
3Diffraction Around Apertures
- Waves spread out when passing through an opening or around an obstacle boundary, with maximum diffraction occurring when the gap width is comparable to the wavelength.
4Wavefronts and Ray Direction
- Wavefronts are lines connecting points of equal phase in a travelling wave, always oriented perpendicular to the direction of wave propagation and rays.
5Transmission
- Sending electricity along power cables from the power station to consumers.
6Critical angle
- Incline angle at which sliding just begins.
7Optically dense
- Having a high refractive index
8Refraction
- Change in direction of light when it changes speed between media.
9Diffraction
- Spreading of waves through a gap or around an edge
10Wavelength
- Distance between a point on one wave and the same point on the next wave
11Boundary
- Surface between two media at which waves are partially reflected
12Wavefront
- Line joining points on a wave that are in step
13Normal
- Line at 90° to a surface.
14n1 sin θ1
n1 sin θ1 n2 sin θ2
What the symbols mean: n = refractive index (no unit) · i or θ1 = angle of incidence · r or θ2 = angle of refraction (both measured from the normal)
Key terms
| Term | Meaning |
|---|---|
| Superposition | Resultant displacement is the sum of individual displacements. |
| Constructive | Waves in phase giving larger amplitude. |
| Destructive | Waves in antiphase giving reduced amplitude. |
| Coherent | Constant phase difference and same frequency. |
| Beats | Periodic variation of amplitude when two nearby frequencies add. |
Avoid these mistakes
1
Adding intensities instead of amplitudes when waves are in phase.
2
Thinking waves destroy each other permanently when they cancel — they emerge unchanged.
3
Forgetting signs when adding displacements.
4
Treating two unrelated sources as coherent.
5
Confusing beat frequency with the average frequency — it is the difference.
Marked practiceQuizzes for this lesson
Last updated:
\n