What is the difference between destructive waves and constractive waves?

Destructive Wave Interference 

During the time when one wave passes through another we say that the waves interfere. When the crest of one wave passes through, or is superpositioned upon, the trough of another wave, we say that the waves destructively interfere. 

During any wave interference the shape of the medium is determined by the sum of the separate amplitudes of each wave. We often say that when waves interfere, amplitudes add. During destructive interference, since the positive amplitudes from one crest are added to the negative amplitudes from the other trough, this addition can look like a subtraction. 

Constructive Wave Interference 

When the crest of one wave passes through, or is superpositioned upon, the crest of another wave, we say that the waves constructively interfere. Constructive interference also occurs when the trough of one wave is superpositioned upon the trough of another wave. 

During any wave interference the shape of the medium is determined by the sum of the separate amplitudes of each wave. We often say that when waves interfere, amplitudes add.

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