Superposition and reflection of waves

Superposition 

A phenomenon like standing waves, diffraction, and interference can be explained by the superposition principle. The superposition principle works on any type of wave such as electromagnetic waves, sound waves, water surface waves, etc. but it works in some conditions. 

Superposition conditions 

The superposition principle is applicable on two waves such that

1. The waves which are being superimposed should be of the same type.
2. The medium in which the waves are traveling should behave linearly i.e. when a portion of a medium has double the displacement, the restoring force is also twice as strong. When the peaks are small, this is frequently the case. For example, little ripples on a pond whose amplitude is far less than their wavelength are a suitable approximation for waves on water.

Superposition types

Based on phase difference, the two superpositions of waves can be classified as

Interference

When two or more waves interfere with each other, then the wave’s amplitude will decrease or increase which depends on the condition such as the medium in which the waves are traveling.

Thomas Young was the first person who noticed light interference in 1801. He used sunlight streaming through two apertures that were closely apart. Young’s double-slit experiment offered the first undeniable proof of light acting as a wave, despite the fact that his source was not really close to being monochromatic.

Constructive Interference 

If the two waves which are traveling in the same medium are superimposed and the two waves are in the same phase then the resulting wave will have constructive interference which means the resulting wave will have a magnitude greater than the two individual waves which are being superimposed.

Destructive Interference 

If the two waves which are traveling in the same medium are superimposed and the two waves are in the opposite phase then the resulting wave will have destructive interference which means the resulting wave will have a magnitude lesser than the two individual waves which are being superimposed.

But in practical situations, the waves are neither in constructive interference nor in destructive interference because the phase of the two waves will not be perfectly in phase or perfectly out of phase. It will be somewhere in the middle.  

Must condition for light interference

The wave sources must be coherent, meaning they must emit similar waves with a fixed phase difference.

The waves should have a single wavelength and be monochromatic.

Phase Difference and path Difference

Phase is defined as the angle between the repetitive cycles of the waves; the phase angle is between 0 to 2 π and (0 to 360). The time period of the wave is given by the portion which is repeated again and again.

When two waves that are coherent in nature are superimposed then the resulting wave will depend on the phase difference of the two waves. If there is no phase difference between the two waves then that means that the two waves are following two different paths and then the phase difference is depending on the length of the path between the waves and that difference is known as the path difference.

The path difference is in the integer multiple of the wavelength which means the waves have interfered constructively. The path difference is in the half-integer multiple of the wavelength which means the waves have interfered destructively inferred:

Phase difference: (2p – 1) π

Path difference = (2p– 1) λ/2

p=integer

K=Kmin

Constructive = K1+K2

Destructive = K1-K2

Intensity and amplitude

When superposition takes place, then it can be easily seen that the two waves which are added up have higher amplitude.

For example, the waves traveling in the lake.

For the waves that have a high frequency, for example sound waves or EM waves, the amplitude of these types of waves can be calculated by calculating the intensity of the wave.

The intensity of a wave can be understood as the energy of the wave in a particular region and that is proportional to the square of the amplitude:

Intensity E A2

Conclusion

The superposition of two waves can be understood as when two waves interfere with each other, the resulting wave may have amplitude more or less depending on the phase difference  and in which medium the waves are traveling.

The phase difference of the waves gives how the two waves are different in the path length. If the amplitude of the two waves is in the same phase then the resulting amplitude will be more and if the resulting amplitude is less than that means the two waves are in the phase opposite to each other. The destructive and constructive waves depend upon the nature of the wave and which direction the wave is moving. If they are in opposite directions, then they are destructive and if they are in the same direction then they are constructive.