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In the field of physics, constructive interference occurs when two waves of the same wavelength are in phase with one another, thus combining their strength. To be in phase, the crests (and troughs) of one wave coincide with the crests (and troughs) of the other.

Here is a visual example of two waves in phase:

        ____              ____
|+     /    \            /    \           
|     /      \          /      \          
|--  /  -  -  \  -  -  /  -  -  \  -  -  / .....
|              \      /          \      /
|-              \    /            \    /
                 ----              ----

        ____              ____
|+     /    \            /    \           
|     /      \          /      \          
|--  /  -  -  \  -  -  /  -  -  \  -  -  / .....
|              \      /          \      /
|-              \    /            \    /
                 ----              ----

The combination of these two waves would be something like this:

        ____              ___
       /    \            /   \
      /      \          /     \
|+    |       |         |      |
|    /        \        /       \
|--  |  -   -  | -   - | -   -  | -   -  | ...
|              |       |        |       |
|-             \      /         \      /
                |     |          |     |
                 \   /            \   /
                  ---              ---

wow... talk about bad ascii art... try to squint when you look at the waves.

If both of these waves existed at the same time in the same direction, the two waves would have constructive interference with each other. As you can see above, when this occurs, the waves combine to essentially form a third wave, which has the combined amplitude of the first two waves; the intensity of this new wave is four times as strong (intensity is amplitude squared).

This effect can easily be demonstrated with two lamps, each with bulbs of identical model and wattage. Put one of the bulbs in the first lamp and turn it on; observe the brightness. Then, put the other bulb in the second lamp and turn that lamp on. If the lamps are close together, you will notice an enhanced brightness, more than you would notice if the bulbs were far apart; this is the added intensity from constructive interference.

Another demonstration of this effect can be done with two people and a piece of string. Have each person hold one end of the string so that it is suspended between the two people, but a bit loose (this string should be fairly long; 50 feet should do). Then each person should whip their arm up and down vertically, creating a "wave" down the string. When the two waves meet, the peak of the wave is much higher than each individual wave; this is constructive interference.

Two more examples come from the audio world from the effects known as tremolo and vibrato. The loudness in the song Crimson and Clover by Tommy James and the Shondells is due to constructive interference (the tremolo effect), for instance; vibrato crops up regularly whenever you hear an extended instrumentation that seems to "pulse"; this, again, is constructive interference at work.

This phenomenon has a related effect called destructive interference which occurs when the waves are completely out of phase.

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