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Wave Motion

Key idea: Compare mechanical and electromagnetic waves, interpret displacement–time and displacement–position graphs, and derive and use v = fλ.

  • GCE A-Level H2 Physics 2027
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Learning objectives

  • Describe wave models, use wave quantities and interpret wave graphs in space and time.
  • Relate phase difference to separations in time and position.

1. Definitions (Must Know)

  • A mechanical wave is a travelling disturbance involving oscillations of particles in a material medium. It cannot travel through a vacuum.
  • An electromagnetic wave consists of oscillating electric and magnetic fields and can travel through a vacuum.
  • A progressive wave transfers energy from one place to another without net transfer of matter.
  • Displacement, y, is a particle’s signed distance from its equilibrium position; amplitude, A, is the maximum magnitude of displacement.
  • Period, T, is the time for one cycle; frequency, f, is the number of cycles per second, so f = 1/T.
  • Wavelength, λ, is the shortest distance between two points in the same phase.

2. Key Ideas (What Earns Marks)

  • In one period T, a progressive wave advances by one wavelength λ: v = λ/T = fλ
  • A displacement–position graph is a snapshot at one instant. Read wavelength along its position axis.
  • A displacement–time graph follows one position. Read period along its time axis.
  • The drawn curve for a longitudinal wave is a graph, not the physical shape of the medium. Particle displacement is parallel to propagation.
  • Particles oscillate locally while the wave pattern and energy propagate; particles do not travel with the wave.
Reading wave graphs in space and timeTwo sinusoidal graphs compare displacement against position at one instant with displacement against time at one location. A longitudinal particle strip underneath shows oscillations parallel to propagation.Snapshot: displacement against positionwavelength λposition xdisplacement yone instant, all positionsTrace: displacement against timeperiod Ttime tdisplacement yone position, all timesLongitudinal wave: particle motion and energy propagationcompression to compression = λenergy travelsparticles oscillate
Scroll diagram horizontally to read all labels.
A displacement–position graph is a snapshot across the medium, so it reveals wavelength. A displacement–time graph follows one particle, so it reveals period. For a longitudinal wave, the plotted displacement is parallel to the direction of travel even though the graph is drawn vertically.
Graph-reading checkpoint

Before reading a horizontal separation, name the axis. A crest-to-crest separation is a wavelength only on a position graph; on a time graph it is a period.

3. Detailed Explanations

A. Deriving v = fλ

Choose a point of constant phase, such as a crest. In time T, that crest travels distance λ: v = distance/time = λ/T Since f = 1/T, this becomes v = fλ.

The relationship describes the speed of the wave pattern. It is not the instantaneous velocity of a particle in the medium.

B. Reading phase from a position graph

At one instant, two points separated by Δ x have phase difference Δφ = 2π(Δ x)/λ provided both points belong to the same progressive wave. Points one wavelength apart are in phase; points half a wavelength apart are in antiphase.

C. Reading phase from a time graph

At one position, two instants separated by Δ t have phase difference Δφ = 2π(Δ t)/T The sign of a lead or lag depends on the order in which the two oscillations are compared, so state the convention if direction matters.

D. Transverse and longitudinal representations

  • In a transverse wave, oscillation is perpendicular to propagation.
  • In a longitudinal wave, oscillation is parallel to propagation; compressions are high-density regions and rarefactions are low-density regions.
  • On a displacement–position graph, the gradient describes how displacement changes with position. It does not show the direction of particle velocity unless the propagation direction is also known.

4. Common Mistakes

  • Calling amplitude the vertical crest-to-trough distance; that distance is 2A.
  • Reading wavelength from a time graph or period from a position graph.
  • Saying particles are carried from source to receiver by a progressive wave.
  • Assuming a steeper drawn wave profile means the wave travels faster; wave speed depends on the medium and fλ, not the drawing’s visual slope.

5. Exam Tips

  • Write the horizontal-axis quantity beside every sketch before identifying T or λ.
  • Convert prefixes before using v = fλ: mathrmkHz to mathrmHz and mathrmmm or mathrmnm to metres.
  • When explaining energy transfer, distinguish particle oscillation from propagation of the disturbance.

6. Worked Examples

Modelled example 1

Wave speed and wavelength

Core

Problem

A sound wave has frequency 680 Hz and speed 340 m s⁻¹. Find its wavelength.
Study the worked solution

  1. Choose the wave relation

    Method

    Use v = fλ.

    Reason

    It connects the propagation speed, cycle rate and distance advanced per cycle.

    Working

    v = fλ

  2. Rearrange and calculate

    Method

    The wavelength is 0.500 m.

    Reason

    Wavelength is the speed divided by cycles per second.

    Working

    λ = v/f = 340/680 = 0.500 m

Common misconception 2

Interpret a longitudinal-wave graph

Find and correct the mistake

Learner claim

A graph shows longitudinal particle displacement vertically against position horizontally. A learner says a point above the axis represents a particle that moved physically upward. Diagnose the claim.

Try this before viewing the solution

View solution step by step

  1. Read the vertical axis

    Method

    The vertical coordinate is a signed displacement value, not a drawing direction in space.

    Reason

    A graph represents how one quantity varies with another; it need not copy the medium’s shape.

    Working

    vertical axis: particle displacement value

  2. Apply the wave type

    Method

    For a longitudinal wave, particle displacement is parallel to propagation.

    Reason

    Longitudinal describes the physical oscillation direction relative to wave travel.

    Working

    oscillation ∥ propagation

  3. Correct the conclusion

    Method

    An above-axis point means positive longitudinal displacement according to the chosen sign convention, not upward motion.

    Reason

    The plotted curve is not the physical outline of the medium.

    Working

    y > 0: positive displacement coordinate

Challenge 3

Distinguish space and time graphs

Minimal support

Independent transfer

Successive crests are 0.24 m apart on a displacement–position graph. At one position, successive crests are 0.015 s apart. Find the wave speed.

Try this before viewing the solution

Unit: m s^-1

Hints

Hint 1: name both horizontal axes
The spatial crest separation is λ; the temporal crest separation is T.
View solution step by step

  1. Extract different quantities

    Method

    λ = 0.24 m and T = 0.015 s.

    Reason

    Crest spacing means wavelength only on a position graph and period only on a time graph.

    Working

    λ = 0.24 m, T = 0.015 s

  2. Convert period to frequency

    Method

    The frequency is 66.7 Hz.

    Reason

    Frequency is the reciprocal of the period.

    Working

    f = 1/T = 66.7 Hz

  3. Calculate wave speed

    Method

    The wave speed is 16 m s⁻¹.

    Reason

    The two representations describe the same progressive wave, so v = fλ combines them.

    Working

    v = (66.7)(0.24) = 16 m s⁻¹

7. Mind Stretchers

Mind stretcher 1: Changing frequency in one mediumExtension

A source frequency doubles while the wave remains in the same non-dispersive medium. Explain what happens to speed and wavelength.

Show Answer

The medium fixes the wave speed, so v is unchanged. From v = fλ, doubling f halves λ.

Continue with the next resource in this course.

Course and syllabus information
Course
GCE A-Level H2 Physics
Edition
GCE A-Level H2 Physics 2027