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What is a progressive wave, and how are its frequency, wavelength, speed and phase related?

Progressive waves and the transfer of energy, amplitude, frequency, wavelength, period, speed and phase, the wave equation, and the difference between transverse and longitudinal waves including polarisation.

A focused answer to AQA A-Level Physics 3.3.1.1 and 3.3.1.2, covering progressive waves and energy transfer, the wave quantities, the wave equation, transverse and longitudinal waves, and polarisation.

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  1. What this dot point is asking
  2. Progressive waves and energy
  3. Describing a wave
  4. The wave equation
  5. Transverse and longitudinal waves
  6. Polarisation
  7. Try this

What this dot point is asking

AQA specification points 3.3.1.1 and 3.3.1.2 want you to define a progressive wave and the quantities that describe it, use the wave equation, distinguish transverse from longitudinal waves, and explain polarisation as evidence that a wave is transverse.

Progressive waves and energy

Describing a wave

Two points exactly one wavelength apart are in phase (phase difference 2π2\pi radians); two points half a wavelength apart are in antiphase (phase difference π\pi radians).

The wave equation

This equation underpins almost every wave calculation: if the speed is fixed by the medium, then increasing the frequency must decrease the wavelength in proportion.

Transverse and longitudinal waves

Polarisation

A plane-polarised wave oscillates in only one plane. Only transverse waves can be polarised, because their oscillations have a definable plane perpendicular to the direction of travel; longitudinal waves cannot, because their oscillations are along the direction of travel. The fact that light can be polarised (for example by a Polaroid filter) is direct evidence that light is transverse. Microwaves and radio waves can also be polarised, which matters for aligning transmitting and receiving aerials so the receiving aerial matches the plane of polarisation.

Try this

Q1. State the wave equation and explain what happens to the wavelength if the frequency doubles at constant speed. [2 marks]

  • Cue. v=fλv = f\lambda; at constant vv, doubling ff halves λ\lambda.

Q2. Explain why the ability to polarise light shows that it is a transverse wave. [2 marks]

  • Cue. Only transverse waves have oscillations that can be restricted to one plane, so polarisation is only possible for transverse waves.

Q3. State the phase difference, in radians, between two points one wavelength apart on a progressive wave. [1 mark]

  • Cue. 2π2\pi radians (they are in phase).

Exam-style practice questions

Practice questions written in the style of AQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

AQA 20193 marksA sound wave of frequency 440 Hz440 \text{ Hz} travels through air at a speed of 340 m s−1340 \text{ m s}^{-1}. Calculate its wavelength and its period.
Show worked answer →

Use the wave equation v=fλv = f\lambda, rearranged to λ=vf=340440=0.77 m\lambda = \dfrac{v}{f} = \dfrac{340}{440} = 0.77 \text{ m}.

The period is the reciprocal of the frequency: T=1f=1440=2.3×10−3 sT = \dfrac{1}{f} = \dfrac{1}{440} = 2.3 \times 10^{-3} \text{ s}.

Markers reward the correct rearrangement of the wave equation for the wavelength and using T=1fT = \dfrac{1}{f} for the period.

AQA 20214 marksExplain what is meant by a transverse wave and a longitudinal wave, and explain why only one of them can be polarised.
Show worked answer →

In a transverse wave the oscillations are perpendicular to the direction of energy transfer (for example light or a wave on a string). In a longitudinal wave the oscillations are parallel to the direction of energy transfer, producing compressions and rarefactions (for example sound).

Only transverse waves can be polarised, because their oscillations occur in a plane perpendicular to the direction of travel, which can be restricted to a single plane. Longitudinal oscillations are along the direction of travel, so there is no perpendicular plane to restrict, and they cannot be polarised.

Markers reward correct definitions of both wave types and explaining polarisation through the perpendicular oscillation plane unique to transverse waves.

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