There are other standing waves, such as on guitar strings and in organ pipes. Waves on the glass of milk are one example of standing waves. The resultant looks like a wave standing in place and, thus, is called a standing wave. If the two waves have the same amplitude and wavelength, then they alternate between constructive and destructive interference. The waves move through each other with their disturbances adding as they go by. These waves are formed by the superposition of two or more moving waves, such as illustrated in Figure 16.36 for two identical waves moving in opposite directions. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. Unmoving waves can be seen on the surface of a glass of milk in a refrigerator, for example. Sometimes waves do not seem to move rather, they just vibrate in place.

Here again, the disturbances add and subtract, producing a more complicated looking wave.įigure 16.35 Superposition of non-identical waves exhibits both constructive and destructive interference. These examples are of waves that are similar.Īn example of the superposition of two dissimilar waves is shown in Figure 16.35. The combined sound can fluctuate up and down in volume as the sound from the two engines varies in time from constructive to destructive. An example of sounds that vary over time from constructive to destructive is found in the combined whine of airplane jets heard by a stationary passenger. A stereo has at least two speakers creating sound waves, and waves can reflect from walls. Varying loudness means the sound waves add partially constructively and partially destructively at different locations. Sound from a stereo, for example, can be loud in one spot and quiet in another. The superposition of most waves produces a combination of constructive and destructive interference and can vary from place to place and time to time. While pure constructive and pure destructive interference do occur, they require precisely aligned identical waves. Because the disturbances are in the opposite direction for this superposition, the resulting amplitude is zero for pure destructive interference-the waves completely cancel.įigure 16.34 Pure destructive interference of two identical waves produces zero amplitude, or complete cancellation. Because the disturbances add, pure constructive interference produces a wave that has twice the amplitude of the individual waves, but has the same wavelength.įigure 16.34 shows two identical waves that arrive exactly out of phase-that is, precisely aligned crest to trough-producing pure destructive interference. This superposition produces pure constructive interference. The crests of the two waves are precisely aligned, as are the troughs. Figure 16.33 and Figure 16.34 illustrate superposition in two special cases, both of which produce simple results.įigure 16.33 shows two identical waves that arrive at the same point exactly in phase. 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. Each disturbance corresponds to a force, and forces add. More specifically, the disturbances of waves are superimposed when they come together-a phenomenon called superposition. When two or more waves arrive at the same point, they superimpose themselves on one another. Luckily, the rules for adding waves are quite simple. Most waves appear complex because they result from several simple waves adding together. Complex waves are more interesting, even beautiful, but they look formidable. (Simple waves may be created by a simple harmonic oscillation, and thus have a sinusoidal shape).

They look more like the waves in Figure 16.32 than like the simple water wave considered in Waves.

(credit: waterborough, Wikimedia Commons) Figure 16.32 These waves result from the superposition of several waves from different sources, producing a complex pattern.

Principle of superposition worksheet