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Superposition and Interference

A wave may have a complicated shape that can result from superposition and interference of several waves.

Learning Objective

  • Distinguish destructive and constructive interference and identify conditions that are required for the superposition of waves


Key Points

    • The disturbances of waves are superimposed when they come together—a phenomenon called superposition.
    • As a result of superposition of waves, inteference can be observed. Interference is an effect caused by two or more waves. Waves can interfere constructively or destructively.
    • The superposition of most waves produces a combination of constructive and destructive interference and can vary from place to place and time to time.

Terms

  • interference

    An effect caused by the superposition of two systems of waves, such as a distortion on a broadcast signal due to atmospheric or other effects.

  • superposition

    The summing of two or more field contributions occupying the same space.


Full Text

Most waves do not look very simple. They look are often more complex than the simple water waves often considered in textbooks . Simple waves may be created by a simple harmonic oscillation, and thus have a sinusoidal shape. Complex waves are more interesting, even beautiful, but they look formidable. Most waves appear complex because they result from several simple waves adding together. Luckily, the rules for adding waves are quite simple.

Complex Pattern of Waves

These waves result from the superposition of several waves from different sources, producing a complex pattern.

Superposition

When two or more waves arrive at the same point, they superimpose themselves on one another. More specifically, the disturbances of waves are superimposed when they come together—a phenomenon called superposition. Each disturbance corresponds to a force, and forces add. If the disturbances are along the same line, then the resulting wave is a simple addition of the disturbances of the individual waves—that is, their amplitudes add.

Interference

As a result of superposition of waves, interference can be observed. Interference is an effect caused by two or more waves .

Wave Interference

A brief introduction to constructive and destructive wave interference and the principle of superposition.

When two identical waves arrive at the same point exactly in phase the crests of the two waves are precisely aligned, as are the troughs . This superposition produces pure constructive interference. Because the disturbances add, constructive interference may produce a wave that has twice the amplitude of the individual waves, but has the same wavelength.

Constructive Interference

Pure constructive interference of two identical waves produces one with twice the amplitude, but the same wavelength.

If two identical waves that arrive exactly out of phase—that is, precisely aligned crest to trough—they may produce pure destructive interference. Because the disturbances are in the opposite direction for this superposition, the resulting amplitude may be zero for destructive interference, and the waves completely cancel.

While pure constructive and pure destructive interference do occur, they require precisely aligned identical waves. The superposition of most waves produces a combination of constructive and destructive interference and can vary from place to place and time to time . Here again, the disturbances add and subtract, producing a more complicated looking wave.

Superposition of Non-Identical Waves

Superposition of non-identical waves exhibits both constructive and destructive interference.

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