Progressive Waves (AQA AS Physics)

• A progressive wave is defined as:

A wave that transfers energy from one point to another without transferring the medium itself

Properties of a Progressive Wave

• 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

• 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 360^o or 2π radians
  • In anti-phase is 180^o or π radians