Constructive Interference

Let us consider that two friends have planned to meet at a specific restaurant on a particular day. The two friends are happy that they are going to meet each other. Then the meeting of the two friends in the restaurant will be considered interference. Interference is a core concept of physics. However, it also has many applications in physics. In layman’s terms when two separate waves coming from two different sources that may not be coherent meet at a particular point then the meeting of the two waves is considered interference. 

Interference definition 

We define interference as the superposition or addition of two or multiple waves which ultimately results in the formation of a new wave pattern. In simple words, we define interference as the interaction between two or more waves. These waves may be coherent or correlated to each other as they might be coming from the same source. This might also happen due to the wave may have the same or almost the same frequency. In this context, it should be discussed that two waves that are non-monochromatic are completely coherent with each other. Each of them has the same difference in phases as well as the same wavelength range at every constituent wavelength. The overall phase difference is derived by adding the initial difference in phase and the path difference (if the generated waves are coming from two or even more sources). Through this, it can be inferred whether the waves coming to the particular point are out of phase also known as destructive interference, or in phase also known as constructive interference. 

Interference waves 

Two waves are said to be interference waves when two or multiple lights or sound waves meet each other. According to the trough and peak alignment, the overlapping waves are liable to cancel each other entirely or partially. Also, the occurrence of destructive or constructive interference takes place only after the two waves have interfered. This happens only as there is a correlation between the two waves that are almost the same or nearly the same frequency or they are coming from the same source. Interference waves can be observed in all kinds of waves namely radio waves, light, gravity waves, matter waves, surface water waves, and so on.

Constructive Interference

Two sound or light waves will experience interference when meeting each other or passing through one another. The individual sounds or light waves add together or superpose for the creation of a new wavefront. Interference can either be constructive interference or destructive interference. Constructive interference specifically occurs when two wave’s maxima add together for that the resultant amplitude of the wave is equal to the sum of the amplitudes of each wave. In constructive interference, the minima of each wave will also be aligned. Here the two waves which interfere have displacement in the same particular direction. Here each of the waves is seen to have upward displacement as the medium through which the waves are traveling has an upward displacement. The constructive interference is mostly observed at locations where both the interfering waves are moving upwards or both of them are moving downwards. 

Constructive interference formula

The constructive interference formula is a specific formula. This formula is given as 

Y1 = Cos (ka – t), and 

Y2 = Cos (ka – t +π/2)

Where k = wave number 

t = time’

a = the position of waves within the time t

ω = frequency

δ = Phase difference  between two waves.

If the frequency of 2 waves within constructive interference is the same then we see that the frequency and amplitude of the resultant wave will be the same. 

Conclusion

The entire article has been written to provide a short note on constructive interference. The topic of constructive interference is very important in the UPSC exam. When two waves coming from the same or opposite direction superpose for forming a resultant wave then interference is said to occur. For understanding the concept of constructive interference firstly we have defined interference. Next interference waves have been analyzed followed by a discussion on constructive interference as well as the constructive interference formula.