AQA A Level Physics

Revision Notes

3.1.1 Progressive Waves

Properties of Oscillations

  • Displacement (x) of a wave is the distance of a point on the wave 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)

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

Diagram showing the amplitude and wavelength of a wave

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

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

Diagram showing the time period of a wave

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

Frequency equation, downloadable AS & A Level Physics revision notes

Frequency-period equation

  • Speed (v) is the distance travelled by the wave per unit time
    • Measured in metres per second (m s-1)
  • The wave equation links the speed, frequency and wavelength of a wave
  • This is relevant for both transverse and longitudinal waves

Wave equation, downloadable AS & A Level Physics revision notes

The Wave Equation

  • The wave equation shows that for a wave of constant speed:
    • As the wavelength increases, the frequency decreases
    • As the wavelength decreases, the frequency increases

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

The relationship between frequency and wavelength of a wave

Worked Example

The wave in the diagram below has a speed of 340 m s–1.

Worked Example: Wave Speed, downloadable AS & A Level Physics revision notes

What is the wavelength of the wave?

Worked example - wave equation, downloadable AS & A Level Physics revision notes

 

Exam Tip

You may also see the wave equation be written as c = where c is the wave speed. However, c is often used to represent a specific speed ー the speed of light (3 × 108 m s–1). Only electromagnetic waves travel at this speed, therefore it’s best practice to use v for any speed that isn’t the speed of light instead.

Phase Difference

  • The phase difference between two waves is a measure of how much a point or a wave is in front or behind another
  • This can be found from the relative positive of the crests or troughs of two different waves of the same frequency
    • 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
  • The diagram below shows the green wave leads the purple wave by ¼ λ

Phase difference, downloadable AS & A Level Physics revision notes

Two waves ¼ λ out of phase

  • In contrast, the purple wave is said to lag behind the green wave by ¼ λ
  • Phase difference is measured in fractions of a wavelength, degrees or radians
  • The phase difference can be calculated from two different points on the same wave or the same point on two different waves
  • The phase difference between two points can be described as:
    • 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.

Worked example - wave properties (1), 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

Worked example - wave properties (2), downloadable AS & A Level Physics revision notes

Exam 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, you will lose marks
  • The same goes for labelling amplitude, don’t draw an arrow from the bottom to the top of the wave, this will lose you marks too.

Author: Katie

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.
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