• 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 ? λ

Two waves ? λ out of phase

• In contrast, the purple wave is said to?lag?behind the green wave by ? 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