Wave Concept

Waves carry energy and momentum from one place to another without the transport of matter.

A wave is a disturbance of a physical property that propagates, such as deformation, pressure, electromagnetic field and so on. We can associate each type of wave with a field.

We can cite the following example: in the case of the free surface of a liquid, the field is the displacement of each point of the free surface of the liquid in relation to the equilibrium form. It is important to have the physical view of a wave as a physical situation described by a "time-dependent field", that is, a function of time.

Interference is one of the characteristics and unique properties of wave motion.

Initial Hypotheses

Unless we explicitly state otherwise, we will make the following assumptions:

1. Continuous Medium
It is when the molecular structure is ignored and a homogeneous medium is admitted. This hypothesis will be valid as long as the spatial fluctuation of the wave (determined by wavelength) is large compared to the intermolecular separation (of the order of 1 ångström, \(10^{-10} m\) ).
2. Perfectly Elastic Medium
Is de medium where the energy of the wave does not decrease as it propagates, since there is no absorption, the amplitude of oscillation does not change.
3. Non-dispersive Medium
Retains the shape of the wave packet.

Classification of Waves

Nature

We know waves of two natures, such as:
Mechanical
Mechanical waves require a mechanical mean to propagate, they do not propagate in vacuum. Example: the sound.
Electromagnetic
Electromagnetic waves can propagate in vacuum and also in some materials. Example: light, radio waves.

Propagation Mode

  
    Transverse     
       Waves where the vibration of the propagation medium is perpendicular to the wave propagation direction. (For example, waves in the strings of a guitar propagate in a transverse way)    
     Longitudinal      
        Waves where the vibration of the propagation medium is in the same direction as the propagation of the wave. (Sound waves propagate in this manner)     
      Mixed       
         It is where the vibration of the propagation medium occurs both on the wave propagation direction and also on the perpendicular direction.  
Illustration of a transverse and a longitudinal wave. The wave at the top of the image (orange line) represents a transverse wave, where the particles oscillate vertically. For example, the waves in the strings of a guitar are transversal. In the lower part is represented a longitudinal wave, where the particles oscillate in the horizontal, the different colors can be thought like variations of pressions present in a wave. For example, sound is a transverse pressure wave propagating in the air.

Dimensions

  
    One-Dimensional     
       Waves that propagate in only one dimension, like the waves on the strings of a guitar.    
     Two-Dimensional      
        Waves that propagate on a surface, like the waves on the canvas of a drum.     
      Three Dimensional
   Waves that propagate in the three dimensions of space, such as sound waves.  

Form

  
    Sinusoid     
       Are those that have trigonometric functions like shape (sine, cosine).    
     Spherical      
        Are those whose wave fronts propagate with spherical symmetry.     
      Cylindrical       
        Are those whose wave fronts propagate with cylindrical symmetry.      
       Flat       
        Are those whose wave fronts are flat.  

Elements of a Wave

Wave Length ( \(\lambda\) )
It is the distance between two consecutive points with same phase.
Period ( \(\tau\) )
It is the time it takes for a wave phenomenon to repeat.
Frequency ( \(f\) or \(\nu\) )
It is the number of times the wave phenomenon is repeated per unit time. The frequency of a wave is always equal to the source that issued it.
Amplitude or Intensity (\(A\))
Amplitude is a scalar measure (negative and positive) of the magnetude of the wave, its value is given by the distance from the origin to the peak of the wave.