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Theme C — Wave Behaviour

C.4 Standing Waves and Resonance — IB Physics SL Revision Notes & Topical Questions

5 min read 10 parts Lesson 21 of 31 1 quiz

📚 IB Physics SL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

C.4 Standing Waves and Resonance — IB PHYSICS SL notes: Explain how standing waves form on strings and in pipes, identify nodes, antinodes and harmonics, and describe resonance and damping.Standing wave — a pattern of fixed nodes and antinodes formed when two identical waves trav…

  • Wavelengths
  • Frequencies
  • First harmonic
  • Closed end
  • Open at both ends
  • Closed at one end

Part 1 of 8Formation of standing waves

Standing wave
  • Standing wave a pattern of fixed nodes and antinodes formed when two identical waves travel in opposite directions and superpose
Formation
  • Formation a wave reflects at a boundary and superposes with the incoming wave
  • At certain frequencies a steady pattern of nodes and antinodes appears.
Energy
  • Energy a standing wave transfers no net energy

Part 2 of 8Nodes and antinodes

1Node
  • Node a point of zero amplitude
2Antinode
  • Antinode a point of maximum amplitude
3Spacing
  • Spacing neighbouring nodes are λ/2 apart
4Phase
  • Phase all points between two adjacent nodes oscillate in phase, and points either side of a node are in antiphase
5Amplitude
  • Amplitude it varies with position from zero at a node to maximum at an antinode

Part 3 of 8Travelling and standing waves compared

FeatureTravelling waveStanding wave
Energy transferYesNo net transfer
AmplitudeSame for all pointsVaries from zero at nodes to maximum at antinodes
PhaseChanges continuously along the waveSame between adjacent nodes; antiphase across a node
WavelengthCrest to crestTwice the node-to-node distance

Part 4 of 8Strings fixed at both ends

1Boundary
  • Boundary there are nodes at both ends
2Wavelengths
  • λn = 2L/n with n = 1, 2, 3 …
3Frequencies
  • Frequencies fn = nv/2L
4First harmonic
  • First harmonic it has one antinode

Part 5 of 8Pipes

Closed end
  • Closed end it is a displacement node
Open end
  • Open end it is a displacement antinode
Open at both ends
  • λn = 2L/n and all harmonics occur
Closed at one end
  • λn = 4L/n with n = 1, 3, 5 … so only odd harmonics occur

Part 6 of 8Finding a harmonic

1
Identify the boundary conditions (node or antinode at each end).
2
Sketch the simplest pattern that fits; this is the first harmonic.
3
Express the length L in terms of λ.
4
Use f = v/λ to find the frequency.
5
Add half-wavelength loops for higher harmonics that still satisfy the boundaries.

Part 7 of 8Resonance

Resonance
Natural frequency
  • Natural frequency the frequency at which a system oscillates when displaced and released
Resonance
  • Resonance the large increase in amplitude when the driving frequency equals the natural frequency
  • Energy is transferred most efficiently at that frequency.
Driven system
  • Driven system it oscillates at the driving frequency
Useful cases
  • Useful cases musical instruments and microwave ovens
Harmful cases
  • Harmful cases bridges and buildings

Part 8 of 8Damping

Damping
  • Damping the loss of energy from an oscillating system due to resistive forces
Light damping
  • Light damping the amplitude decays gradually over many cycles
Critical damping
  • Critical damping the system returns to equilibrium in the shortest time without oscillating
Heavy damping
  • Heavy damping the system returns slowly without oscillating
Resonance curve
  • Resonance curve more damping lowers and broadens the peak and shifts it to a slightly lower frequency

Key terms

TermMeaning
Standing waveA pattern formed by two identical waves travelling in opposite directions, with fixed nodes and antinodes.
NodeA point of zero amplitude in a standing wave.
AntinodeA point of maximum amplitude in a standing wave.
HarmonicA mode of vibration whose frequency is a whole-number multiple of the first harmonic.
Natural frequencyThe frequency at which a system oscillates when displaced and released.
ResonanceThe large increase in amplitude when the driving frequency equals the natural frequency.
DampingThe loss of energy from an oscillating system due to resistive forces.
Critical dampingDamping that returns a system to equilibrium in the shortest time without oscillation.

Avoid these mistakes

Avoid these mistakes
Taking the node spacing as one wavelength — it is half a wavelength.
Using the open-pipe harmonic series for a pipe closed at one end.
Saying a standing wave transfers energy along the string.

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