Superposition and progressive and stationary waves

We all know how the energy is transferred in the wave. Yes it is due to the disturbance in the particles from its equilibrium position. So today lets discuss a new and interesting topic. Superposition theorem states that "If the large  waves are passing from a medium then the displacement of the resultant of the particle of the medium is given by the sum of vectorial of all the displacement of the particles through it by the waves." This theorem is very important and is used in the circuit analysis during which different amount of the charge is made to flow. In this way it plays an important role. Now then after lets talk about the waves the two major waves that we gonna focus today is progressive and stationary wave.
Progressive waves are also known as the travelling waves as they travel in a forward direction. They are the waves in which the crest and trough as well as the compression as well as the rarefaction travel in a straight line or in a forward direction. According to this the crest and the trough possess the equal velocity to those of the waves. The characteristics of the progressive waves are as follows.
1. The amplitude of the waves are same in all the condition.
2. No particles is permanently at rest.
3. The maximum values for the velocity of  all the medium are the same.
  
        Stationary waves are those waves that are formed as the result of superimpose of the two progressed waves travelling in a opposite direction but with the same velocity. There is no flow of the energy and if we observe it then we feel no movement of the waves thus is named as the stationary waves.
  The point to where the amplitude is 0 then it is called as the nodes. Similarly the point at which the amplitude is maximum is called antinode This are the two terms of the stationary waves which is the key to understand the wave more clearly. The characteristic of the stationary waves are as follows.
1. The amplitudes in this case is different at different places in the medium.
2. In this case the particles are seem to be not moving and hence is called the stationary waves.
3. The particles at the nodes are permanently at rest.
4. The velocity at different particles are different but the velocity of the particles are nodes is 0 since it is consider as the minimum velocity.
     This are the all the definition and the characteristics of the wave.