# The Wave Equation

## Overview of Wave Motion

• A wave is a disturbance that travels through a medium, transferring energy from one point to another.
• Waves can be classified into two types: mechanical waves, which require a medium to travel, such as sound waves; and electromagnetic waves, which can travel through space, like light and radio waves.
• Each wave has specific properties: amplitude, frequency, wavelength, and speed, which describe its motion and behaviour.

## Properties of Waves

• Amplitude is the maximum displacement or distance moved by a point on the wave from its equilibrium position.
• Frequency is the number of occurrences of a repeating event per unit of time. It is measured in hertz (Hz).
• Wavelength is the shortest distance between two points in a wave’s shape, such as peak to peak or trough to trough.
• Wave Speed is the speed at which the wave pattern moves through space. It is measured in metres per second (m/s).

## The Wave Equation

• The wave equation is a mathematical formula used to represent wave motion.
• The wave equation relates the speed of the wave (v) to its frequency (f) and wavelength (λ) using the following formula: `v = f * λ`.

## Understanding the Wave Equation

• The speed of the wave (v) is equal to the frequency (f) times the wavelength (λ). If we know any two parameters, we can calculate the third.
• Increasing the frequency of a wave, while keeping the speed constant, would decrease the wavelength and vice versa.
• The units used in the wave equation are: speed (m/s), frequency (Hz), and wavelength (m).

## Practical Applications

• The wave equation is essential in fields like physics, engineering, and communications as it provides significant information about the wave and its behaviour.
• It is used to predict the behaviour of waves, calculate the wavelength or frequency of a wave, and understand wave interactions such as interference and diffraction.

## Revision Tips

• Memorise the wave equation: `v = f * λ`. Understanding what each symbol stands for will help you use the equation effectively.
• Understand that all types of waves, whether sound, light, or radio, follow the wave equation.
• Regularly practice problems involving the wave equation to strengthen your understanding and problem-solving skills.

Remember, understanding and being able to apply the wave equation is a key aspect of the principles and applications of science.