- 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)
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)
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
- 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
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
The relationship between frequency and wavelength of a wave
The wave in the diagram below has a speed of 340 m s–1.
What is the wavelength of the wave?
You may also see the wave equation be written as c = fλ 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.
- 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
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
Plane waves on the surface of water at a particular instant are represented by the diagram below.
The waves have a frequency of 2.5 Hz.
a) The amplitude
b) The wavelength
c) The phase difference between points A and B
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.