Properties of Waves

The four main wave properties are:

  • Wavelength
  • Amplitude
  • Frequency
  • Period

Below you can see two displacement-time graphs which show the properties of waves:

Two graphical representations of waves. On the left, a wave is plotted against time in seconds, with the vertical axis showing displacement. The peak to peak distance of the wave is labelled as 'Period', and the maximum height of the wave is labelled as 'Amplitude'. On the right, a similar wave is plotted against distance in metres. The distance between two consecutive peaks is labelled as 'Wavelength', and again, the maximum height is labelled as 'Amplitude'. Both waves transition from blue to red, indicating a change over time or distance.

  • Keep in mind that displacement indicates how far the wave has oscillated from the equilibrium point.

Wavelength

Wavelength (λ) is the distance between two peaks that are next to each other, or any two identical points that are next to each other. In the ‘Properties of waves’ diagram above, the wavelength is measured at the midpoint, not the peak.

Amplitude

Amplitude is the maximum displacement of a point on the wave. It is the distance between the midpoint and the peak of the wave, or the midpoint and the trough of the wave.

Frequency

Frequency is the number of complete waves passing a point in a second. The wave equation below shows how wave speed, frequency and wavelength are related.

An equation in cursive font stating "wave speed equals frequency multiplied by wavelength".

An equation showing the letter 'v' equals the letter 'f' multiplied by the Greek letter 'lambda'.

  • v = Wave speed in metres per second (m/s)
  • f = Frequency in hertz (Hz)
  • λ (lambda) = Wavelength in metres (m)

Time Period

The time period of a wave is the time taken for a full cycle of a wave. This can be calculated when the frequency value is known. The equation to work out the time period of a wave is:

A mathematical equation stating that "time period" is equal to 1 divided by "frequency".
A formula expressing that capital "T" is equal to the inverse of lowercase "f".
  • T = Time period in seconds (s)
  • f = Frequency in hertz (Hz)

Example

A wave has a wave speed of 255 m/s and a wavelength of 15 m. Calculate the time period of the wave.

Step 1: Identify the known values

Wave speed = 255 m/s

Wavelength  = 15 m

Step 2: Put the known values into the equation to calculate the frequency

We know that wave speed = frequency × wavelength

By rearranging the equation, we can calculate the frequency. So, frequency = \frac{wave\:speed}{wavelength}\frac{wave\:speed}{wavelength}

Frequency = \frac{255}{15}\frac{255}{15}

= 17 Hz

Step 3: Put the known values into the equation to calculate the time period

Time period = \frac{1}{frequency}

= \frac{1}{17}\frac{1}{17}

Time period = 0.0588 s (3 s.f.)

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