Interference

When two waves traveling in the same medium in opposite direction meet at a certain point, they form a wave with larger amplitude or smaller amplitude or displacement. This resulting wave is due to a phenomenon called the interference of waves. The displacement of the wave during interference is the sum of the amplitudes of the two or more interacting waves. After every interference, the waves continue traveling in the medium towards their direction. In all the figures, the arrow above indicates the direction of the wave, whether to the right or to the left. 

Interference may be constructive or destructive.

Constructive interference happens when two waves traveling in opposite direction but with the same direction of displacement interact. A bigger wave will be produced at a certain point where the two interacting waves meet up. In a constructive interference, the amplitude of the resulting wave formed during interference is always greater than any of the amplitude of the two interfering waves. To analyze and understand more about constructive interference, see figures below.


Example 1 - Constructive Interference.

Given are two waves with upward displaced wave pulse. Suppose the first wave \(1\; \text{unit}\) of displacement is traveling to the right and the second wave traveling to the left displaced to \(2\;\text{units}\)


 


The resulting wave amplitude during interference is equal to

\(A_1 + A_2 = 1\;\text{unit} + 2\;\text{units}=3\;\text{units}\).


Example 2 - Constructive Interference

Two wave displaced \(1\;\text{unit}\) downward, results to a wave with two units downward during interference as shown below.

 

\(A_1 +A_2 = (-1\;\text{unit})+(-1\;\text{unit})=-2\;\text{units}\)

The negative sign indicates the downward direction of the displacement of the waves. 


Destructive interference is produced by the meeting up of two waves traveling in the same medium at different direction and also displaced in opposite direction. The amplitude wave produced during interference is still the sum of the two interfering waves. The only difference between the two types of interference is that, in the destructive interference, the displacement of the wave are in opposite direction, thus they also have different signs resulting to the subtraction of the amplitudes of the waves. The ampitude of the resulting wave during interference is less than the amplitude of the larger interfering wave. 


Example 3 - Destructive Interference

A wave displaces \(2\;\text{units}\) upward meets another wave with \(1\;\text{unit}\) displaced wave pulse.

The wave produced between the interfering wave is

\(A_1+A_2=2\;\text{units}+(-1\;\text{unit})=1\;\text{unit}\).

The direction of displacement of the wave during interference is upward.


Example 4 - Destructive Interference

Two waves traveling in the same medium has the same amount of \(1\;\text{unit}\) displacement in opposite direction, as in the figure below, the two waves totally cancel out each other resulting to a zero displacement of the wave produced during interference.

 

 

  \(A_1 + A_2=1\;\text{unit} + (-1\;\text{unit})=0\)