Crests:   A 'crest' is the point on a wave with the maximum value or upward displacement within a cycle

Troughs:    A trough is the opposite of a crest, so the minimum or lowest point in a cycle

Period:  Period is the duration of time it takes for a wave to complete one cycle of oscillation.

Frequency:  Frequency refers to how many waves are made per time interval. This is usually described as how many waves are made per second, or as cycles per second.

Amplitude: Highest or lowest possible measurement of displacement of the wave from equilibrium. 

Wavelength: The wavelength of a wave is the distance between any two adjacent corresponding locations on the wave train. This distance is usually measured in one of three ways:  Crest to the next crest, trough to next trough, or from the start of a wave cycle to the next starting point.

Interference: The adding of the amplitude of two or more waves "combining" at a   point in space

Medium:   A medium is a substance or material that carries the wave. The wave medium is   not the wave   and it doesn't make the wave; it merely carries or transports the wave from its source to other locations. In the case of our slinky wave, the medium through that the wave travels is the slinky coils. In the case of a water wave in the ocean, the medium through which the wave travels is the ocean water. In the case of a sound wave moving from the church choir to the pews, the medium through which the sound wave travels is the air in the room.

Wave Front:   The set of points in space reached by a wave or vibration at the same instant as the wave travels through a medium. Wave fronts generally form a continuous line or surface. The lines formed by crests of ripples on a pond, for example, correspond to curved wave fronts.

Ray:   In physics, term denoting the straight line along which light or other types of waves propagates from its source. It generally refers to the line of propagation of waves but is also applied to streams of particles such as the electrons emitted from a cathode or particles emitted by substances exhibiting radioactivity. A ray is drawn perpendicular to the wave front.

Sine Wave:   A typical method of representing a property of a wave is as a sine wave.   When a sine wave is used to represent a wave, were only looking at a single property such a displacement, energy, or in the case of light electric or magnetic field strength.

      Mechanical waves are a local oscillation of material. Only the energy propagates; the oscillating material does not move far from its initial equilibrium position; the wave travels by jumping from one particle of the medium to another. Therefore, mechanical waves transport energy and not material;

     A mechanical wave requires an initial energy input to be created. Once this initial energy is added, the wave will travel through the medium until all the energy has been transferred.

     There are 4 types of mechanical waves.  

     Transverse waves (important) are waves that cause the medium to vibrate at a 90-degree angle to the direction of the wave. Two parts of the wave are the crest and the trough. The crest is the highest point of the wave and the trough is the lowest. The wavelength is the distance from crest to crest or from trough to trough.

     The next type is longitudinal waves (important). A longitudinal wave is much like a Slinky. When the particles the wave is traveling through are close together, it is called compression. When the particles it is traveling through are spread apart, it is called rarefaction. Sound waves are an excellent of longitudinal waves.

     Another type of heat wave is a abdominal wave (not important, don't study). This type of wave is the wave that twists along a given medium. An example would be: if a force twists a coil on one end, and released, the "twist" will travel completely through the wave and end up on the other side.

     The final type of wave is a surface wave (not important, don't study). This type of wave travels along a surface that is between two media. An example of a surface wave would be waves in a pool, or in an ocean.

Definition provided by wikipedia

Vocabulary  

         Light waves are a little more complicated then mechanical waves, and they do not need a medium to travel through (very, very important). They can travel through a vacuum. A light wave consists of energy in the form of electric and magnetic fields. The fields vibrate at right angles to the direction of movement of the wave, and at right angles to each other. Because light has both electric and magnetic fields, it is also referred to as electromagnetic radiation.

         Light waves come in many sizes. The size of a wave is measured as its wavelength, which is the distance between any two corresponding points on successive waves, usually peak-to-peak or trough-to-trough. The wavelengths of the light we can see range from 400 to 700 billionths of a meter. But the full range of wavelengths included in the definition of electromagnetic radiation extends from one billionth of a meter, as in gamma rays, to centimeters and meters, as in radio waves. Visible light is one small part of the spectrum. It is also important to point out that in fields of study other then physics the word "light" refers to only the visible light spectrum, where in physics "light" is the entire spectrum (from gamma and x rays to radio waves)

Definition provided by How stuff works.

Vocabulary 

Matter waves, also called de Broglie waves, are the wave-like nature of all matter, including the atoms that make up your body. One of the first and most important findings of quantum physics is that electrons have a dual wave-particle nature. It soon became apparent that all matter has this dual nature, but because conventional matter has a high momentum relative to electrons, the wavelength of the matter waves is very small, and in most cases barely noticeable. For instance, the wavelength of the matter that makes up a person is on the order of 10^{−35 meters}, far smaller than can be observed using current measurement technologies.

Definition provided by Wise Geek