Question

Wave A has an amplitude of 2 and wave B has an amplitude of 2 as shown below. What will happen when the crest of wave A meets the trough of wave B? They will interfere to create a crest with an amplitude of 4. They will interfere to create a crest with an amplitude of 2. They will interfere to create a crest with an amplitude of 0. They will bounce off each another.

Answer 1

Since the two waves have equal amplitudes, if the crest of one wave
meets the trough of the other one, they'll add to produce a level of zero
at that location.

Answer 2

The correct answer to the question is- They will interfere to create a crest with an amplitude of 0.

EXPLANATION:

Before going to answer this question, first we have to understand destructive interference.

The two super imposing waves are said to be doing destructive interference if the crest of one wave falls on the trough of another wave.

Let the amplitudes of  two waves are A and B.

The phases difference $(\theta)$ will be 180 degree for destructive interference.

Hence,the amplitude of the resultant wave is calculated as -

                                          R =  $\sqrt{A^2+B^2+2ABcos\theta}$

                                             = $\sqrt{A^2+B^2+2ABcos180}$

                                             = $\sqrt{A^2+B^2-2AB}$

                                             = $A-B$

Here, the amplitude of first wave A = 2

  The amplitude of second wave B = 2

Hence, amplitude of resultant wave R = 2-2

                                                                = 0

Hence, the correct answer will be - They will interfere to create a crest with an amplitude of 0.