Consider a transverse wave moving through a medium. For example, a wave moving through a stretched spring.

Each point in the medium is oscillating in a direction perpendicular to the direction of propagation of the wave. (If the wave is a sine wave, the oscillation of each point is the simplest type of oscillation, called simple harmonic motion.)

The points are all oscillating but different points reach their maximum displacement at different times. To describe this situation we say that a wave consists of many oscillations which are out of phase with each other. The actual phase difference between two oscillations depends on the distance between them (measured along the direction of propagation of the wave).

In many situations, we need to consider two sets of waves of the same frequency travelling through the same medium.

The combined effect of the two waves at a given point in the medium will depend on the phase difference between their oscillations at the point considered.

The two waves are said to interfere constructively or destructively as illustrated by the diagrams below.

Two waves arriving at a point in phase with each other: constructive interference.

The resultant of these two oscillations will be an oscillation of amplitude equal to sum of the amplitudes of the two original oscillations.

Two waves arriving at a point in anti-phase with each other: destructive interference.

In this case the algebraic sum of the oscillations results in an oscillation of smaller amplitude. If the amplitudes of the two oscillations are equal the result is no oscillation.

The fact that the resultant amplitude can be found by adding together the individual amplitudes is sometimes referred to as the principle of superposition of waves.

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