Properties of Waves (DP IB Physics)

Properties of Waves

• Travelling waves are defined as follows:

Oscillations that transfer energy from one place to another without transferring matter

• Waves transfer energy, not matter

• Waves are generated by oscillating sources 

  • These oscillations travel away from the source

• Oscillations can propagate through a medium (e.g. air, water) or in vacuum (i.e. no particles), depending on the type of wave

• The key properties of travelling waves are as follows:

Displacement

• Displacement  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

  • Measured in metres (m)

Wavelength

• Wavelength λ is the length of one complete oscillation measured from the same point on two consecutive waves 

  • For example, two crests, or two troughs

  • Measured in metres (m)

Amplitude

• Amplitude A is the maximum displacement of an oscillating wave from its equilibrium position (x = 0)

  • Amplitude can be positive or negative depending on the direction of the displacement 

  • Measured in metres (m)

  • Where the wave has 0 amplitude (the horizontal line) is referred to as the equilibrium position

Diagram showing the amplitude and wavelength of a wave

Period & Frequency

• Period (T) is the time taken for a complete oscillation to pass a fixed point

  • Measured in seconds (s)

• Frequency (f) is the number of complete oscillations to pass a fixed point per second

  • Measured in Hertz (Hz)

• The frequency, f, and the period, T, of a travelling wave are related to each other by the equation:

• Where:

  • f = frequency (Hz)

  • T = time period (s)

Period T and frequency f of a travelling wave

Wave speed

• Wave speed (v) is the distance travelled by the wave per unit time

  • Measured in metres per second (m s^-1)

• The wave speed is defined by the equation:

• Where:

  • v = wave speed (m s^–1)

  • λ = wavelength (m)

• This is referred to as the wave equation

• It tells us that for a wave of constant speed:

  • As the wavelength increases, the frequency decreases

  • As the wavelength decreases, the frequency increases

The relationship between the frequency and wavelength of a wave