Interference of Waves

When a wave interferes with another wave, the medium takes on a shape that is dictated by a mixture of the net effects caused by both individual waves on the particles in the medium, rather than by the individual waves themselves. 

When two or more waves interfere with one another, the concept of superposition is used to analyse how much interference there is between them. Wave propagation interference is a phenomenon that occurs when two waves clash while travelling through the same medium at the same time. 

What happens when two waves interfere?

You may be wondering what would happen when two waves travelling in the same medium come into contact with each other. The resulting wave’s frequency or amplitude will change. It is also possible that problems may emerge about whether the nature of two waves meeting will alter. 

Depending on how the waves overlap and how their peaks and troughs align, interference can be defined as the phenomenon in which two or more waves collide and superpose to form a resultant wave with a greater, lower, or the same amplitude depending on how they collide and superpose and how they align their peaks and troughs. 

Whenever two or more waves reach at the same place while travelling in the same medium, they superimpose themselves on one another, or, more accurately, the disturbances of the waves superimpose on one another when they arrive at the same location. Because we know that forces add up, we may relate each of these disruptions to a particular force. This is analogous to how two forces operating in the same direction add up to form a wave. This means that when two waves are added together, the total amplitude of the resulting wave is obtained. 

The Principle of Linear Superposition

According to the principle of linear superposition, which can be applied to any number of waves, when two or more waves of the same type are incident on a point, the resultant amplitude at that point is equal to the vector sum of each of the individual waves. To simplify matters, consider what happens when two waves collide. 

Interference of sound waves examples include music reaching you simultaneously from two distinct sources, or two pulses moving in the same direction down a string at the same time When these waves combine, the outcome is a set of superimposed waves that add up, with the amplitude at any given position equal to the sum of the amplitudes of the individual waves at that place. Despite the fact that these waves interfere with one another when they meet, they continue on their journey as if they had never met one another. 

Many types of waves have been seen to display this behaviour, including waves on a string, sound waves, and surface water waves, among others. Electromagnetic waves likewise follow the superposition principle, however instead of the displacement of the medium, the electric and magnetic fields of the combined wave are joined together to create the wave. Linear waves are defined as waves that obey the superposition principle; nonlinear waves, on the other hand, are defined as waves that do not follow the superposition principle. 

Constructive Interference

This form of interference is referred to as “productive interference” in certain circles. When two interfering waves have a displacement in the same direction, it is called constructive interference. It may occur anywhere along the medium’s length, and it can occur at any time. This is because both waves have an upward displacement in this scenario, and as a result of this, the medium has an upward displacement that is larger than the difference between the two interfering pulses. In any site where the two interfering waves are pushed upward from one another, constructive interference is detected. However, it may also be detected when both interfering waves are pushed downward at the same time. 

Destructive Interference

Destructive interference is a sort of interference that may occur anywhere along the medium’s length when the two interfering waves have a displacement in the opposite direction of one another. Suppose a sine pulse with maximum displacement of one unit encounters another sine pulse with maximum displacement of one unit, and the result is destructive interference. 

Reflection of waves

This is true for both pulses and periodic waves, however it’s a little easier to observe the difference with pulses. Take, for example, what happens when a pulse hits the end of its rope, to put it another way. The wave will be reflected back to the shore along the fishing line. 

As long as the end is stationary, a 180° phase shift will occur, which is the opposite of what happens when the end is moved. 

If the end is free, the pulse returns in the same direction as it went out (so no phase change). 

If the pulse travels along one rope that is linked to another rope that has a different density than the first, part of the energy is transported into the second rope and some of the energy is returned. Assuming that the end of the light rope is fixed, the reflection happens for a pulse travelling from it to a heavy rope. When looking at it from a distance, it seems as though the end is completely free. 

Standing waves

Consider a wave travelling over a string that is fixed at one end, which is relevant to musical instruments. After passing through the end, the wave will be reflected back, and since the end was fixed, the reflection will be 180° in the opposite direction of the original wave (also known as a 180° phase change). The reflected wave will interfere with the portion of the wave that is still travelling towards the fixed end. Normal interference will be neither wholly constructive nor totally destructive, and nothing of value will result as a result of the interaction. Occasionally, though, when the wavelength of the light is matched to the length of the string, the outcome may be quite beneficial in certain situations. 

Conclusion

A wave’s interference with another wave causes the medium to assume a form that is determined by a combination of the net effects produced by both individual waves on the particles in the medium. 

With respect to mechanical waves, the principle of superposition states that when two or more travelling waves combine at the same point, the resulting position of the mass element of the medium at that point is the algebraic sum of the positions due to each individual wave. The resultant wave is just the sum of the disturbances of the individual waves if they are all in the same direction.