Two waves with the same frequency
have a phase difference of 360 degrees. Which of the following is the
interference produced by the waves? (A) Constructive interference, (B)
destructive interference, (C) neither constructive nor destructive interference.
Here, this problem tells us there
are two waves with the same frequencies with a phase difference of 360 degrees. We are asked to figure out what
kind of interference is produced by the waves when they interact with each
other. In order to solve this problem, we
should refresh our memories on how waves interact with each other in space. When two waves are occupying the
same space at the same time, they will interfere with each other. If they have the same frequency,
they will have a constant phase difference as they travel.
We are told that the two waves do
have the same frequency in this problem, so they will have a constant phase
difference throughout their interaction. There are two types of interference
that can occur: constructive interference or destructive interference. Constructive interference happens
when the interfering waves have a phase difference of zero. Notice how the highs and lows of
the two waves match up. This means the resulting wave will
have an amplitude equal to the sum of the amplitude of the two waves.
On the other hand, when the waves
have a phase difference of 180 degrees, so that the peaks of one wave line up with
the troughs of the other, they will interfere destructively. Notice how the highs and lows of
these waves are opposite of each other. This will cause the equal
amplitudes of the waves to cancel each other out like we see here, and the resulting
wave will have an amplitude of zero. We′ve seen that the phase
difference of waves that interfere destructively is 180 degrees. The phase difference of
constructively interfering waves is zero degrees, which is the same as a phase
difference of 360 degrees.
We are told that the waves in this
example have a phase difference of 360 degrees. Therefore, there will be
constructive interference between these two waves when they meet in space. So, the first option, constructive
interference, is the correct answer.