Progressive Waves (AQA A Level Physics): Revision Note

Properties of oscillations

• 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)

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

  • Measured in seconds (s)

• Frequency (f) is the number of complete oscillations per unit time

  • Measured in Hertz (Hz) or s^-1

  • It can be calculated using the following equation:

$f=\frac{1}{T}$

• 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 and is given by:

$v=f\lambda$

• This is relevant for both transverse and longitudinal waves

• 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

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 position 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 two waves with the same wavelength and frequency, but they are not in phase

• The green wave reaches the same point in the cycle (e.g. a peak) earlier than the purple wave — it is shifted to the left

• This means the green wave leads the purple wave by ¼ λ

• 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