Wave equation (AQA GCSE Physics): Revision Notes
Wave equation
The wave equation is one of the most important relationships in physics. It shows us how three key wave properties are connected together for any type of wave.
What is the wave equation?
The wave equation tells us the relationship between wave speed, frequency, and wavelength. Every wave - whether it travels through air, water, or solid materials - follows this same pattern.
The beauty of the wave equation is its universality - it applies to all types of waves in nature, from the tiniest light waves to massive seismic waves moving through the Earth.
The equation works for all types of waves:
- Sound waves travelling through air
- Water waves on the surface of a pond
- Light waves travelling through space
- Seismic waves moving through the Earth
The wave equation formula
The wave equation is written as:
wave speed = frequency × wavelength
Or using symbols:
Where:
- v = wave speed (measured in metres per second, m/s)
- f = frequency (measured in hertz, Hz)
- λ (lambda) = wavelength (measured in metres, m)
This equation tells us that if you know any two of these values, you can calculate the third one.
Rearranging the equation
Sometimes you need to find frequency or wavelength instead of speed. You can rearrange the equation:
- To find wavelength:
- To find frequency:
- To find wave speed:
Triangle Method Tip
A useful way to remember this is with a triangle method - cover up the value you want to find and the remaining letters show you what to do. Draw a triangle with at the top and and at the bottom.
Typical wave values
Different types of waves have very different speeds and properties:
| Wave type | Speed (m/s) | Frequency (Hz) | Wavelength (m) |
|---|---|---|---|
| Sound | 340 | 3000 | 0.11 |
| Water | 5 | 5 | 1.0 |
| Light | 3 × 10⁸ | 6 × 10¹⁴ | 5 × 10⁻⁷ |
| Seismic | 4000 | 40 | 100 |
These typical values help you check if your calculations make sense. If you calculate a sound wave travelling at the speed of light, you know something has gone wrong!
Working with the equation
When solving wave equation problems, follow these essential steps:
- Write down what you know - identify the given values
- Choose the right version of the equation
- Substitute the numbers carefully
- Check your units - make sure they match up correctly
- Calculate and check your answer makes sense
Worked Example: Finding Wavelength
If a seismic wave travels at 4050 m/s and has a frequency of 15 Hz, what is its wavelength?
Step 1: Write down what we know
- Wave speed () = 4050 m/s
- Frequency () = 15 Hz
- Wavelength () = ?
Step 2: Choose the right equation We want to find wavelength, so use:
Step 3: Substitute the numbers
Step 4: Check the answer 270 m is a reasonable wavelength for a seismic wave - it matches our typical values table.
Always remember to include the correct units in your final answer.
Units and conversions
Pay Careful Attention to Units
- Wave speed is always in m/s (metres per second)
- Frequency is always in Hz (hertz, which means "per second")
- Wavelength is always in m (metres)
Sometimes you might need to convert units. For example, if wavelength is given in centimetres, convert to metres by dividing by 100.
Common exam questions
Typical Exam Questions
You might be asked to:
- Calculate wave speed when given frequency and wavelength
- Find frequency when given speed and wavelength
- Determine wavelength when given speed and frequency
- Use typical values to solve problems about specific wave types
The key is identifying which version of the equation to use and making sure your units are correct.
Remember!
Key Points to Remember:
- The wave equation applies to ALL types of waves - sound, light, water, seismic
- - wave speed equals frequency times wavelength
- Units matter - always check they're correct (m/s, Hz, m)
- Rearrange carefully - cover the unknown value to see what calculation to do
- Check your answer - does it match typical values for that wave type?