Question

Wave A has an amplitude of 2, and wave B has an amplitude of 2. 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 0.
They will interfere to create a crest with an amplitude of 2.
They will interfere to create a crest with an amplitude of 4.
They will bounce off each another.

Answer 1

Answer:

They will interfere to create a crest with an amplitude of 0.

Explanation:

It is given that,

Wave A has an amplitude of 2, and wave B has an amplitude of 2. The superposition of two waves is called interference of wave. When the resultant wave have maximum amplitude is called constructive interference while when the amplitude of resultant completely destructs, the destructive interference happens.    

When the crest of wave A meets the trough of wave B, then destructive interference occurs. the phase difference will be 180°. There resultant is given by :

$R=\sqrt{A^2+B^2+2ABcos(180)}$

R = A - B

Here A = 2 and B = 2

⇒ R = 0

Hence, the correct option is (a) "They will interfere to create a crest with an amplitude of 0".

Answer 2

They will interfere to create a crest with an amplitude of 0 as it’s basically addition so 2 + (-2) would equal 0 as they cancel out