IB Physics SL C.4 Standing waves and resonance Questions

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Use standing-wave diagrams to track phase and amplitude, calculate allowed frequencies in strings and pipes, and compare resonance and damping responses.

57 questions in this syllabus scope, with question parts counted together.

Syllabus
First assessment 2025
Course
Physics SL
Level
SL
Exam points & syllabus

Exam points

  • Explain a standing wave by tracing incident and reflected waves travelling in opposite directions and stating that their displacements superpose.
  • Compare standing and travelling waves using net energy transfer, position-dependent amplitude or phase; do not confuse those properties with formation.
  • Use fixed nodes and antinodes to compare amplitude and phase: particles share frequency, while different loops can reverse phase and change amplitude.
  • Translate longitudinal displacement graphs into actual particle positions and velocities along the tube, using successive profiles when direction is needed.
  • After half a period, reverse the standing-wave displacement profile while preserving displacement magnitude and node positions.
  • Infer wavelength from repeated nodes or antinodes using λ/2 spacing; count intervals rather than marked points before applying v=fλ.
  • Relate sand piles to longitudinal standing waves: air motion moves sand away from displacement antinodes towards displacement nodes.
  • For the stated weaker-reflection sound experiment, explain reduced contrast through lower maxima and higher minima at unchanged positions.
  • Choose displacement boundary conditions before fitting a mode: fixed or closed ends are nodes, while free or open ends are antinodes.
  • Use half-wavelength loops for fixed-fixed strings and open-open pipes; use odd quarter-wavelength sections for closed-open pipes.
  • Scale fixed-string harmonic frequencies with loop number, using a known mode to calculate another frequency or draw its node-preserving shape.
  • For a closed-open pipe, use odd multiples of the first frequency; reject a proposed even multiple when it cannot satisfy the open-end antinode.
  • Use consecutive closed-open resonance gaps: length gaps are λ/2 at fixed frequency, while frequency gaps are 2f₁ at fixed length.
  • Combine mode geometry with v=fλ and graph timing to determine wave speed, frequency or pipe length, including required units and precision.
  • Compare resonators by equating their allowed frequencies; use harmonic number and boundary conditions to determine relative lengths.
  • Separate geometry from wave speed: shorter air columns raise first frequency, while higher speed at fixed length raises frequency with unchanged wavelength.
  • Count end antinodes when interpreting an open-open pipe: two internal nodes indicate its second mode and λ=L.
  • Excite the first string mode by driving at its first resonant frequency or plucking its middle; distinguish this from identifying the resulting pattern.
  • Define resonance by frequency matching, then locate the amplitude-response maximum at or near the system’s natural frequency.
  • Apply frequency matching to a valid lattice absorption model, and identify machinery vibration as a case where resonance should be avoided.
  • Distinguish free decay from driven response: small friction reduces free-oscillation amplitude over time while its period is approximately unchanged.
  • With greater damping, lower the driven response curve and its peak; place the peak at lower driving frequency within the sketch’s accepted tolerance.
  • Recognise critical damping as minimum return time without overshoot; distinguish light frequency stability and the broad shifted heavy-response peak.
  • Choose small damping where persistent oscillation is useful, as in a quartz oscillator, and distinguish this from suppressing structural vibrations.

Covered syllabus points

C.4.1—Standing wave formationC.4.2—Nodes and antinodesC.4.3—Strings and pipesC.4.4—ResonanceC.4.5—Damping and resonanceC.4.6—Types of damping

Question 1

[Maximum number: 2]

A loudspeaker emits sound of frequency 210 Hz into a pipe with one open and one closed end. The diagram shows a representation of the standing wave established in the pipe.

Figure for Question 1 — IB Physics SL

Outline how the standing wave is formed in the pipe.

Question 1

[Maximum number: 2]

Question (a)

(a)

The solid line represents the standing wave at time t and the dotted line represents the standing wave at an instant later. The dot is the equilibrium position of a particle P in the pipe. The up arrow indicates displacements to the right and the down arrow displacements to the left.

Figure for Question (a) — IB Physics SL

On the diagram, draw

[ 2 ]

Question (i)

(i)

a dot to indicate the approximate position of P at time t,

[ 1 ]

Question (ii)

(ii)

an arrow to indicate the velocity of P at time t.

[ 1 ]

Question (b)

(b)

A loudspeaker emits sound of frequency 210 Hz into a pipe with one open and one closed end. The diagram shows a representation of the standing wave established in the pipe.

Figure for Question (b) — IB Physics SL
[ 1 ]

Question (i)

(i)

Determine the wavelength of the wave.

[ 1 ]

Question (c)

(c)

The frequency of sound is reduced to 140 Hz . Explain why a standing wave will not be formed in the pipe.

[ 2 ]

Question 1

[Maximum number: 2]

Question (a)

(a)

The solid line represents the standing wave at time t and the dotted line represents the standing wave at an instant later. The dot is the equilibrium position of a particle P in the pipe. The up arrow indicates displacements to the right and the down arrow displacements to the left.

Figure for Question (a) — IB Physics SL

On the diagram, draw

[ 2 ]

Question (i)

(i)

a dot to indicate the approximate position of P at time t,

[ 1 ]

Question (ii)

(ii)

an arrow to indicate the velocity of P at time t.

[ 1 ]

Question (b)

(b)

A loudspeaker emits sound of frequency 210 Hz into a pipe with one open and one closed end. The diagram shows a representation of the standing wave established in the pipe.

Figure for Question (b) — IB Physics SL
[ 1 ]

Question (i)

(i)

Determine the wavelength of the wave.

[ 1 ]

Question (c)

(c)

The frequency of sound is reduced to 140 Hz . Explain why a standing wave will not be formed in the pipe.

[ 2 ]

Question 1

[Maximum number: 2]

This question is in two parts. Part 1 is about solar radiation and the greenhouse effect. Part 2 is about a mass on a spring.

Part 1 Solar radiation and the greenhouse effect
The following data are available.

Table for Question 1 — IB Physics SL

Point P now begins to move from side to side with a small amplitude and at a variable driving frequency f. The frictional force is still small.

At each value of f, the object eventually reaches a constant amplitude A.
The graph shows the variation with f of A.

Figure for Question 1 — IB Physics SL

With reference to resonance and resonant frequency, comment on the shape of the graph.

Question 1

[Maximum number: 4]

This question is in two parts. Part 1 is about solar radiation and the greenhouse effect. Part 2 is about a mass on a spring.

Part 1 Solar radiation and the greenhouse effect
The following data are available.

Table for Question 1 — IB Physics SL

Question (a)

(a)

The sketch graph below shows how the displacement of the object from point O varies with time over three time periods.

Figure for Question (a) — IB Physics SL
[ 2 ]

Question (i)

(i)

Sketch on the same axes a graph of how the displacement varies with time if a small frictional force acts on the object.

[ 2 ]

Question (b)

(b)

Point P now begins to move from side to side with a small amplitude and at a variable driving frequency f. The frictional force is still small.

At each value of f, the object eventually reaches a constant amplitude A.
The graph shows the variation with f of A.

Figure for Question (b) — IB Physics SL
[ 2 ]

Question (i)

(i)

On the same axes, draw a graph to show the variation with f of A when the frictional force acting on the object is increased.

[ 2 ]

Question 1

[Maximum number: 2]

This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity

Simple harmonic motion and waves

W in (a) is immersed in a beaker of oil. As a result of this immersion the oscillations of W are critically damped. Describe what is meant by critically damped.