Wave equation (AQA GCSE Physics Combined Science): Revision Notes

Wave equation

What is the wave equation?

The wave equation is a simple formula that connects three important properties of any wave. It shows how wave speed, frequency and wavelength are related to each other.

This equation works for all types of waves - whether they're sound waves, light waves, water waves or earthquake waves.

The wave equation formula

The wave equation is written as:

$v = f \lambda$

Where:

• v = wave speed (measured in m/s)
• f = frequency (measured in Hz)
• λ = wavelength (measured in m)

Understanding the variables

Wave speed (v) is how fast the wave travels through a material or space. It's measured in metres per second (m/s).

Frequency (f) is how many waves pass a point every second. It's measured in hertz (Hz), which means "per second".

Wavelength (λ) is the distance between two identical points on a wave, like from one peak to the next peak. It's measured in metres (m).

Rearranging the equation

You can rearrange the wave equation to find any of the three values:

• To find wavelength: $\lambda = \frac{v}{f}$
• To find frequency: $f = \frac{v}{\lambda}$
• To find wave speed: $v = f \lambda$

Typical wave values

Different types of waves have very different speeds and properties:

• Sound waves in air: speed = 340 m/s, frequency = 3000 Hz, wavelength = 0.11 m
• Water waves: speed = 5 m/s, frequency = 5 Hz, wavelength = 1.0 m
• Light waves: speed = $3 \times 10^8$ m/s, frequency = $6 \times 10^{14}$ Hz, wavelength = $5 \times 10^{-7}$ m
• Seismic S-waves: speed = 4000 m/s, frequency = 40 Hz, wavelength = 100 m

How to solve wave equation problems

Example calculations

Units are important