# 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) 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 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 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

#### Worked Example

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

#### What is the wavelength of the wave?

#### 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 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. 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

#### 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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