Question Video: Identifying the Definition of Constructive Interference | Nagwa Question Video: Identifying the Definition of Constructive Interference | Nagwa

# Question Video: Identifying the Definition of Constructive Interference Physics • Second Year of Secondary School

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Which of the following statements correctly defines constructive interference? [A] Constructive interference of two waves occurs when the resultant wave has zero amplitude. [B] Constructive interference of two waves occurs when the resultant wave has an amplitude equal to the average of the amplitudes of the two waves. [C] Constructive interference of two waves occurs when the resultant wave has an amplitude equal to the sum of the amplitudes of the two waves. [D] Constructive interference of two waves occurs when the resultant wave has an amplitude equal to the difference of the amplitudes of the two waves.

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### Video Transcript

Which of the following statements correctly defines constructive interference? (A) Constructive interference of two waves occurs when the resultant wave has zero amplitude. (B) Constructive interference of two waves occurs when the resultant wave has an amplitude equal to the average of the amplitudes of the two waves. (C) Constructive interference of two waves occurs when the resultant wave has an amplitude equal to the sum of the amplitudes of the two waves. (D) Constructive interference of two waves occurs when the resultant wave has an amplitude equal to the difference of the amplitudes of the two waves.

In this question, we are asked to pick the statement out of these four options that correctly defines constructive interference. Let’s first remind ourselves what interference is and how we can know what kind of interference will occur.

When two waves occupy the same space at the same time, they will interfere with each other. This interference can be constructive or destructive, which means the resultant amplitude will either be larger or smaller than the original amplitudes.

Constructive interference occurs when there is a phase difference of zero between the two waves. And the amplitude of the resultant wave will be larger than the original two waves. Notice how the troughs and the peaks of the two waves line up when there will be constructive interference. The resultant wave’s amplitude will be the amplitudes of the original waves added together.

Destructive interference occurs when there is a phase difference of 180 degrees and the peaks and troughs of the two waves are opposite each other like seen here. The amplitudes of the two waves also add together. But since one wave always has an opposite negative amplitude of the other, they will cancel each other out. And we are left with a resultant wave with an amplitude of zero.

Let’s take a look at the options we are given and figure out if they are true or not. The first option says that when two waves have constructive interference, the resultant wave has an amplitude of zero. We know this is what happens with destructive interference, not constructive, so this is not the right answer.

The next option says that when two waves experience constructive interference, the resultant wave will have an amplitude equal to the average of the two waves. But we know the amplitude of a resultant wave from constructive interference is the sum of the two waves. So this option is also not the correct answer.

The third option says that when two waves interfere constructively, the amplitude of the resultant wave is equal to the sum of the two waves that interfered. This is a true statement. The resultant wave’s amplitude will be equal to the amplitudes of the two waves added together.

Just to be sure though, let’s have a look at the fourth option and make sure it is false like the first two. This option says the resultant wave from two waves constructively interfering will be equal to the difference between the amplitudes of the two waves. This is false. We know that the sum of the two amplitudes of the interfering waves is equal to the resultant wave’s amplitude.

This means that the third option — constructive interference of two waves occurs when the resultant wave has an amplitude equal to the sum of the amplitudes of the two waves — is the correct answer.

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