Waves

Waves are the transfer of energy from one place to another in the form of a periodic disturbance. For example, when a stone is thrown onto a water surface, water molecules on the surface move up and down. As a water molecule moves it collides with the nearest water molecule and transfers energy to that molecule, thus setting it in motion.

Transverse and Longitudinal waves

There are two types of waves: Transverse and Longitudinal Waves.:

Transverse Waves are waves that vibrate perpendicular to the direction of travel of the wave. Examples of Transverse Waves include, but are certainly not limited, to: Electro-Magnetic Waves*, Sine and Cosine Waves,and the wave of a string.
Longitudinal Waves are waves that vibrate parallel to the direction of travel of the wave. They are also commonly referred to as Pressure or Compression Waves. Longitudinal waves include sound waves, (Although you wouldn't know it if you looked at sound waves on an osciliscope!) and the waves of a spring or slinky pulled back and forth

Electromagnetic Waves can travel through a vacuum. These waves are unique because they do not need a medium of travel unlike all other waves. Light and heat are examples of electromagnetic waves. Electromagnetic Waves travel at the speed of light and have no mass.

Equation for Velocity and Wavelength

V=\lambda f\,

In this equation:

f is the frequency (The number of peaks to pass a point in a given time, usually in Hz)
λ (The Greek letter lambda) is the wavelength (usually measured in meters)
V is the resulting velocity in m/s (meters per second). Wave speed is equal to the frequency times the wave length.

It can be understood as how frequently a certain distance is transversed.

Medium

A medium is a substance through which a wave can travel. For example: Sound waves need a medium. It travels by the vibration of liquid,solid and gas.

Although some soundtrack wave can travel without a medium. For example: Visible light

Resources

w: Waves in plasmas