Frequency, Wavelength and Speed

Understanding frequency, wavelength and speed is fundamental to everything around us. From noise and vibration, chatter on a lathe tool to the light we experience from objects.

Waves move energy from one place to another without any accompanying matter. Sound waves, ocean waves and electromagnetic waves are some of the examples; other, more complicated types of waves can spread in plasmas All waves have 4 basic properties which they exhibit; Reflection, Refraction, Diffraction and Interference.

An ocean traveller has even more vividly the impression that the ocean is made of waves than that it is made of water.

Arthur S. Eddington

The relationship between frequency, wavelength and speed in any material is easy to express as an equation.

frequency wave speed wavelength equation


c = wave speed [ms-1]

f = frequency [Hz]

k = wavenumber [m-1]

λ = wavelength [m]

Sometimes though it is good to visualise it.

Shear Wave

shear wave

The axis of vibration is perpendicular to the direction of propagation of the wave. With this, the bonding between the particles within the solid experiences shearing forces.

Wavelength: the distance between successive peaks in the perpendicular motion of the particles of the medium at an instant of time.

Longitudinal Wave

longitudinal wave

A wave in which the vibrations of the medium are parallel to the direction the wave is moving.

Wavelength: the distance from the start of one compression or rarefaction to the start of the next compression or rarefaction at an instant of time.

Angular Frequency – the frequency of a steady recurring phenomenum in radians per second. Also known as Circular Frequency.

Crest – the peak of a wave disturbance.

Peak to Peak Value – the over-all amplitude of a signal measured from its lowest (or most negative) peak to its most highest (or most positive) peak.

Peak Value – the instantaneous maximum value of a waveform.

Trough – a valley of a wave disturbance.

Wavenumber – describes the spatial variation of waves, phase change per unit distance

Further reading

  1. BBC Bitesize – Features of Waves
  2. BBC Bitesize – Properties of Waves
  3. Wikipedia – Wavelength

speed of sound proportional to square root of temperature

Speed of Sound

The speed of sound depends on the elastic and inertial properties of the particular medium.

In air, the speed of sound depends on the temperature of the air, at 20°C the speed of sound is 343ms-1.

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