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.

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 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.

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).

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.

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.