Properties of waves

Waves are one of the ways in which energy may be transferred between stores. Waves can be described as oscillations, or vibrations about a rest position. For example:

  • sound waves cause air particles to vibrate back and forth
  • ripples cause water particles to vibrate up and down

The direction of these oscillations is the difference between longitudinal or transverse waves. In longitudinal waves, the vibrations are parallel to the direction of wave travel. In transverse waves, the vibrations are at right angles to the direction of wave travel.

Mechanical waves travel through matter. They cause oscillations of particles in a solid, liquid or gas. The material through which they travel is called a medium. Electromagnetic waves cause oscillations in electrical and magnetic fields. They do not need matter to travel through.

curriculum-key-fact
All waves transfer energy but they do not transfer matter.

Parts of a wave

Waves are described using the following terms:

  • Rest position - the undisturbed position of particles or fields when they are not vibrating.
  • Displacement - the distance that a certain point in the medium has moved from its rest position.
  • Peak - the highest point above the rest position.
  • Trough - the lowest point below the rest position.
  • Amplitude - the maximum displacement of a point of a wave from its rest position.
  • Wavelength - distance covered by a full cycle of the wave. Usually measured from peak to peak, or trough to trough.
  • Time period - the time taken for a full cycle of the wave. Usually measured from peak to peak, or trough to trough.
  • Frequency - the number of waves passing a point each second.

Diagram of a wave

A displacement time graph of a mechanical wave with labelled key features

Wave period and wave speed

The time period of a wave can be calculated using the equation:

\text{Time period} = \frac{1}{\text{frequency}}

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

This is when:

  • time period (T) is measured in seconds (s)
  • frequency (f) is measured in hertz (Hz)

Example calculation

Calculate the time period of a wave with a frequency of 50 Hz.

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

\text{T} = \frac{1}{50}

\text{T} = 0.02 s

Question

Calculate the time period of a wave with a frequency of 400 Hz.

\text{T} = \frac{1}{400}

\text{T} = 0.0025 s

Calculating wave speed

The speed of a wave is how fast the wave moves through the medium.

The speed of a wave can be calculated using the equation:

wave speed = frequency × wavelength

\text{v} = \text{f \lambda}

This is when:

  • wave speed (v) is measured in metres per second (m/s)
  • frequency (f) is measured in hertz (Hz)
  • wavelength (λ) is measured in metres (m)
Formula triangle demonstrating v equals f times lambda. V at the apex of triangle, f in bottom-left corner and lambda in bottom-right. Also demonstrates f equals v over lambda, lambda equals v over f.

Example calculation

What is the speed of a wave that has a frequency of 50 Hz and a wavelength of 6 m?

\text{v} = \text{f \lambda}

\text{v} = 50 × 6

\text{v} = 300 m/s

Question

What is the speed of a wave with a frequency of 0.2 Hz and a wavelength of 25 m?

\text{v} = \text{f \lambda }

\text{v} = 0.2 × 25

\text{v} = 5 m/s