Waves: properties, types and equations

​​In a nutshell

The properties of a wave are amplitude, wavelength, frequency, time period and wave speed. Wave speed can be related to frequency and wavelength using the wave speed equation. Transverse and longitudinal waves behave differently.

Equations

Variable Definitions

Properties of a wave

A transverse wave is a wave that undulates at right angles to the direction it is travelling in.

1. Oscillations 2. Trough 3. Wavelength 4. Crest 5. Amplitude 6. Direction of travel/energy transfer

Time period

The period of a wave is how long a wavelength takes to travel through a point. This can be found using the equation

​$$period = \frac{1}{frequency}\\ \ \\ T = \frac{1}{f}$$​​

Tip: Rearrange this equation to make frequency the subject! You can use this in questions to work out the frequency when only given the time period.

Transverse and longitudinal

The two types of wave are transverse and longitudinal.

Transverse waves oscillate (undulate) perpendicular to the direction of energy transfer. The direction of energy transfer is the same as the direction the wave travels in. 

Example

Electromagnetic wave or a wave on a string.

Longitudinal waves oscillate parallel to the direction of energy transfer. They are made up of compressions and rarefactions. Compressions are where the particles in the vibrating medium are closest together. Rarefactions are where the particles are furthest apart.

1. Wavelength 2. Compression 3. Rarefaction 4. Direction of travel and energy transfer 5. Oscillations

Example

Sound wave or a P-type seismic wave.

Wave speed equation

Frequency and wavelength can be related together by the wave speed equation. The wave speed can be described as the speed of the wave, as well as the speed at which energy is transferred.

​$$wave \space speed = frequency \times wavelength\\ \ \\v = f\times \lambda$$​​

Example

A wave has a frequency of $$5\,Hz$$​ and a wavelength of $$20\,cm$$​. What is its wave speed?

First, write down the quantities given and check they are in the correct form:

$$f = 5\,Hz\\ \ \\ \lambda = 20 \,cm = \frac{20}{100} = 0.2\,m$$

Next, write down the equation you will need to use:

$$v = f \times \lambda$$​​

Then, substitute the values into the equation:

$$v = 5 \times 0.2 = 1$$

Make sure to include the units:

$$wave\ speed, v = 1\, m/s$$​​

The wave speed of the wave is ​$$\underline{1\,m/s}$$.​

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