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.
