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First teaching 2023

First exams 2025

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Progressive Waves (CIE A Level Physics)

Revision Note

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Wave motion

  • Energy is transferred through moving oscillations or vibrations.
    • These can be seen in vibrations of ropes or springs

Vibrations of ropes or springs

Wave on rope and spring, downloadable AS & A Level Physics revision notes

Waves can be shown through vibrations in ropes or springs

  • The oscillations / vibrations can be perpendicular or parallel to the direction of wave travel:
    • When they are perpendicular, they are transverse waves
    • When they are parallel, they are longitudinal waves

Ripple tanks

  • Ripple tanks may be used to demonstrate the wave properties of reflection, refraction and diffraction.
    • The paddle produces a combination of transverse and longitudinal waves

A ripple tank

ripple-tank-ruler-and-paddle

Wave effects can be demonstrated using a ripple tank - the taller regions of water block more light, allowing the wavefronts to be seen using shadows 

General wave properties

  • Displacement (x) of a wave is the distance from its equilibrium position. It is a vector quantity; it can be positive or negative
  • Amplitude (A) is the maximum displacement of a particle in the wave from its equilibrium position
  • Wavelength (λ) is the distance between points on successive oscillations of the wave that are in phase
    • These are all measured in metres (m)

 Graph showing displacement of a wave against distance

Amplitude and wavelength, downloadable AS & A Level Physics revision notes

Wavelength is the distance between two identical points on the wave and amplitude is maximum displacement from equilibrium position

  • Period (T) or time period, is the time taken for one complete oscillation or cycle of the wave
    • Measured in seconds (s)

Graph showing displacement of a wave against time 

Displacement time wave, downloadable AS & A Level Physics revision notes

When the x axis is time, the separation between two identical points on the wave is the period of the wave, not the wavelength. Look out for the quantity on the x axis.

  • Frequency f is the number of complete oscillations per unit time
    • Measured in Hertz (Hz) or s-1

f space equals space 1 over T

  • Where T is the time period of the oscillation, measured in seconds (s)
  • Speed v is the distance travelled by the wave per unit time
    • Measured in metres per second (m s-1)

Phase difference

  • The phase difference tells us how much a point or a wave is in front or behind another
    • When the crests or troughs are aligned, the waves are in phase
    • When the crest of one wave aligns with the trough of another, they are in antiphase
    • This can be found from the relative positions of the crests or troughs of two different waves of the same frequency
  • The diagram below shows that
    • the green wave leads the purple wave by ¼ λ
    • the purple wave is said to lag behind the green wave by ¼ λ

Displacement time graph shows phase difference

Phase difference, downloadable AS & A Level Physics revision notes

Two waves ¼ λ out of phase

  • Phase difference is measured in fractions of a wavelength, degrees or radians
  • The phase difference between two points is:
    • In phase is 360o or 2π radians
    • In anti-phase is 180o or π radians

Worked example

Plane waves on the surface of water at a particular instant are represented by the diagram below.

WE - Wave properties question image, downloadable AS & A Level Physics revision notes

The waves have a frequency of 2.5 Hz.

Determine:

(a)
the amplitude
(b)
the wavelength
(c)
the phase difference between points A and B
 

Answer:

(a) Determine the amplitude:

  • Amplitude is the maximum displacement from equilibrium position:

A space equals space fraction numerator 7.50 over denominator 2 end fraction space equals space 3.75 space mm

(b) Determine the wavelength:

  • Recall that a wavelength is the distance between two identical points in a wave
  • From the diagram, 25 cm covers 3 full wavelengths and three quarters of the next wavelength

lambda space equals space fraction numerator 25 over denominator 3.75 end fraction space equals space 6.7 space cm

(c) Find the phase difference between A and B:

  • The distance between points A and B is half a wavelength
  • One wavelength is a phase difference of 360°
  • Half a wavelength is a phase difference of 180°

Examiner Tip

When labelling the wavelength and time period on a diagram, make sure that your arrows go from the very top of a wave to the very top of the next one. If your arrow is too short or just near to the crest, you will lose marks. The same goes for labelling amplitude.

Wave energy

  • Waves that transfer energy are known as progressive waves
  • Progressive waves transfer energy between points, without transferring matter
  • When a progressive wave travels between two points, no matter actually travels with it
    • The points on the wave simply vibrate back and forth about fixed positions

  • Waves that do not transfer energy are known as stationary waves

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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.