3.1 General properties of waves

Waves are disturbances that transfer energy from one place to another. A key characteristic of waves is that they do not transfer matter. Instead, the particles of the medium simply oscillate around their mean position, carrying the energy along.

Energy Transfer

Waves are a common way for energy to be transported. Consider a wave in water. The water molecules don't travel long distances with the wave; they just move up and down. The energy, however, propagates outwards.

Types of Waves

There are different types of waves, each with its own characteristics. The two main categories are:

• Transverse Waves: In transverse waves, the displacement of the particles is perpendicular to the direction of wave propagation. A water wave is a good example.
• Longitudinal Waves: In longitudinal waves, the displacement of the particles is parallel to the direction of wave propagation. Sound waves are longitudinal waves.

Wave Properties

Waves have several key properties that describe their behaviour:

• Wavelength (λ): The distance between two consecutive crests or troughs of a wave.
• Amplitude (A): The maximum displacement of a particle from its mean position. It is related to the wave's intensity (energy).
• Frequency (f): The number of complete waves that pass a point in one second, measured in Hertz (Hz).
• Period (T): The time taken for one complete wave to pass a point, which is the reciprocal of the frequency ($T = \frac{1}{f}$).
• Wave Speed (v): The speed at which the wave propagates, related to wavelength and frequency by the equation: $v = f \times λ$

Table of Wave Properties

Property	Symbol	Unit	Description
Wavelength	λ	m	Distance between two successive crests or troughs.
Amplitude	A	m	Maximum displacement from the mean position.
Frequency	f	Hz	Number of waves passing a point per second.
Period	T	s	Time for one complete wave cycle.
Wave Speed	v	m/s	Speed at which the wave propagates.

Important Note: The energy carried by a wave is directly proportional to the square of its amplitude. This means a larger amplitude wave carries significantly more energy.