What happens when two sound waves meet in constructive interference?

Question

micelarnyiz · Accepted Answer

Anytime two waves travel through the same space, their amplitudes add at all points, this is known as interference.Constructive interference specifically refers to situations where the resulting amplitude is larger than either of the initial two amplitudes.
If you have two amplitudes

a_{1}

and

a_{2}

which add to form

A = a_{1} + a_{2}

then:
For constructive interference,

A = a_{1} + a_{2} | A | > | a_{1} |, | a_{2} |

For destructive interference,

a_{1} + a_{2} = 0

If two waves interfere constructively at all points, they are said to be "in phase." A simple example of this would be adding two sine waves together:

a_{1} = \sin (x)

a_{2} = \sin (x)

It should be obvious that these two waves interfere perfectly constructively, resulting in a single wave that is twice as big as either of them individually:

A = a_{1} + a_{2} = \sin (x) + \sin (x) = 2 \sin (x)

A final useful note is that though this question involved sound waves, interference works in the same way for all waves, including electromagnetic waves or the statistical wavefunctions of quantum mechanics.

What happens when two sound waves meet in constructive interference?

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