Video Transcript
The diagram shows the wave fronts
of two waves that have been diffracted through equally narrow gaps. Both waves have the same speed,
wavelength, frequency, and initial displacement as each other. At which of the points shown is the
interference between the waves constructive? (A) Point A only. (B) Point B only. (C) Point C only. (D) Points A and B only. Or (E) all the points except C.
In this question, we have two light
waves that have each been diffracted through a narrow gap. This diagram uses lines to
represent their wave fronts. And thus, for each light wave, the
distance between each pair of successive wave fronts is equal to one wavelength.
It’s important to note that we’ve
been told that these two light waves are nearly identical, since they have the same
initial displacement, wavelength, frequency, and therefore speed. The only real difference is that
the light wave shown in orange passed through the gap on the left, and the light
wave shown in blue passed through the gap on the right. We know that where the two waves
meet, they’ll interfere with each other. So let’s briefly remind ourselves
about wave interference and how to discern between constructive and destructive
interference.
Constructive interference occurs
when two waves are in phase, meaning their crests and troughs coincide, or match up,
and add to create even greater crests and troughs. Here, it’ll be helpful to recall
that waves interfere constructively if the distance that they have traveled from
their gap is different by an integer number of their wavelengths: zero, one, two, or
three, and so on.
On the other hand, destructive
interference occurs when two waves are out of phase, meaning the crests of one wave
match up with the troughs of the other, meaning they’ll add to zero. In other words, the interference
will be destructive if the distances from the two gaps at a point is different by
half a wavelength, or three-halves, five-halves, and so on.
Okay, now that we’ve reviewed wave
interference, let’s take a closer look at the points labeled in the diagram. Starting with point A, we can see
that two wave fronts are crossing here. More specifically, each wave has
traveled a distance of two wavelengths from its respective gap. Thus, there is no difference in the
distances traveled between the two waves. So they’re in phase, and we know
that there is constructive interference at point A.
In fact, for this question, because
we know that each wave front represents an integer wavelength of distance from a
gap, there must be constructive interference at any point that lies directly on two
wave fronts. Knowing this, we can tell that
points B and D also mark points of constructive interference. But what about point C? It lies on a wave front of the wave
shown in orange. But it lies halfway between two
wave fronts of the wave shown in blue. Thus, we know that there is a half
wavelength difference between the distances the waves traveled from the gaps. And thus, there’s destructive
interference at point C.
So we’ve found that there’s
constructive interference at points A, B, and D, but not at point C. And therefore, the correct answer
is option (E). The interference between the waves
is constructive at all the labeled points except C.
