# The Wave Equation

# 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.