Objectives:

• To understand the terms constructive interference and destructive interference in terms of path difference and phase difference
• To witness, and understand the reasons for, two source interference with sound and microwaves

A recap on constructive and destructive interference

When two waves meet, they interfere and they superpose. There are two special cases, where the two waves have the same frequency and are coherent. When they interfere they can have a constructive interference and a destructive interference.

Constructive interference occurs when the two waves superpose at the right time to give the maximum superposition, while destructive interference the minimum.

If you look at the figure above, the constructive interference occurs when the lines of the two diffracted waves meet and there is a cross of lines. There the constructive interference occurs, as the superposition occurs when both waves are at maximum peak. The destructive interference occurs when the line of one wave is exactly half way between two lines of the other wave. So basically where there is the red line in between two black lines. This occurs when the rays are $180$ degrees out of phase.

If we looked are constructive and destructive interference from the point of view of path difference, when two rays have a path difference of an integer number of wavelengths, it means that the rays are coherent and in phase, which means that constructive interference occurs. They may have started at different times so one has traveled longer, hence the path difference, but in this case the two waves will go up at the same time and go down at the same time. This means that they are in phase and they undergo constructive interference. Instead, if the path difference is a $1.5$ or $latex2.5$ or $3.5$ and so on number of wavelengths, this means that the two rays are travelling in anti-phase and that destructive interference occurs. More generally, if the path difference is:

$\Delta \lambda = n \lambda$

then constructive interference occurs, while if the path difference is:

$\Delta \lambda = (n+\frac{1}{2}) \lambda$

then destructive interference occurs.

For more information on interferences due to two or more waves, watch the following clip:

Page co-written with Luca Quinci – Thank you!

Further reading: