We encounter waves everyday in our lives and they might be in the form of earthquake waves, electromagnetic waves, heat waves, light waves, mechanical waves, microwaves, radio waves, shock waves, sine waves, sound waves, sports stadium waves, vibrating string waves and water waves. Radiation is the method that allows energy to move from one place to another in the form of waves.  Waves spread out in all directions from every point on the disturbance that created them and they are often caused by vibrating objects.  The kinetic energy that is released into the water when a stone is dropped into it will radiate away in circular waves.  Energy radiates from a source to a target. Waves are periodical disturbances which are propagated through a particular medium.  Most waves have two main parts where the top is called the crest and the bottom is called the trough.  A crest is often followed by second crest, which is again followed by the next crest.  The high point of a wave is its crest can be viewed as being separated by the trough and this will generate a pattern of crests and troughs.

The maximum displacement of a particle by a wave is called amplitude and the wavelength is the distance between two adjacent crests of a wave.  The period is the time it takes for one full vibration of a particle in a medium and frequency is the inverse of a period.  A surface wave is a disturbance at the boundary between two media.  A longitudinal wave occurs when particle motion is parallel to wave motion.  A transverse wave occurs when particle motion is perpendicular to wave motion.  When a transverse wave is moving from right to left the individual particles in the medium are moving up and down.  The wave front of a longitudinal wave radiates outward from its source, while the particles vibrate back and forth about their original positions.

Interference is the combination of two or more waves that results in a single wave.  When interference decreases amplitude it is called destructive interference.  Interference that increases amplitude is called constructive interference.  Diffraction is the change in direction of a wave when it encounters an obstacle or edge.  A traveling wave is a wave in which the medium moves in the direction of propagation.  A standing wave is a pattern of vibration that resembles a stationary wave. Standing waves appear to stay in one place they do not look like they are moving through a medium.  Picture a string, or cord, or chain, or cable that is vibrating, it is possible to get it to vibrate in a manner where you are generating a wave, but this wave is not propagating, it is not building.  It is just sitting there vibrating up and down in one place.  Nodes are the points in a standing wave that have no vibration due to destructive interference.

A wave doesn’t just stop when it reaches the end of the medium.  Reflection occurs when a wave bounces back after meeting a surface or boundary and refraction is the bending of waves as they pass from one medium to another at an angle.  The principle of superposition is a method of adding crests and troughs of interfering waves together to describe a new wave.  The French scientist and mathematician Jean Baptiste Fourier (1768–1830) proved the mathematical fact that any periodic waveform can be expressed as the sum of an infinite set of sine waves.  Sine waves and cosine waves are both sinusoidal waves, and Fourier gave us the foundation to change square waves into these sinusoidal waves.