In Concept 1 below, we show what occurs when two peaks like the ones in the illustration above combine. We show the result at four
successive times. A blue pulse is traveling from left to right and a red pulse is traveling in the opposite direction. You can see that at each
instant the combined pulse is determined by adding the vertical displacements of the two pulses at every point along the string.
In the description above, we are applying the principle of superposition: The wave that results when two or more waves combine can be
determined by adding the displacements of the individual waves at every point in the medium. This is sometimes more tersely stated as: The
resulting wave is the algebraic sum of the displacements of the waves that cause it. (“Algebraic” means that you add positive and negative
displacements as you would any signed numbers; no trigonometry is required.)
You see this principle in play in Concept 1. For instance, when the two peaks meet at time t = 2.5 s, the resulting peak’s displacement equals
the sum of the displacements of the two separate peaks. This is an example of constructive interference, which occurs when the amplitude of a
combined pulse or wave is greater than the amplitude of any individual pulse or wave.
In Concept 2 below, a peak meets a trough. Except for the different directions of displacement, the pulses are identical. The two pulses cancel
out completely when they occupy the same location on the string, and the string momentarily has zero displacement at each point. Positive and
negative displacements of the same magnitude sum to zero. This is destructive interference: The amplitude of the combined pulse or wave is
less than the amplitude of either individual pulse or wave.
You may have experimented with this in the introduction simulation, but if you did not, you can go back and see what happens when peak
meets peak, when peak meets trough, and finally, when two troughs meet. The result in each case is that the combined displacement is the
sum of the displacements of all the pulses.
When the string is “flat” in Concept 2, it may seem there is no motion because you are looking at a static diagram. In fact, some of the string
particles are moving up and some are moving down. The particles that were part of a peak are moving down and will be part of a trough. This
is readily witnessed in the introductory simulation.
In this section, we used transverse wave pulses on a string to illustrate superposition, but the principle of superposition can also be applied to
longitudinal waves (for instance, the combined sound wave produced by two stereo speakers). Acoustical (sound) engineers rely on
constructive interference to create louder sounds and destructive interference to mask noises. For instance, noise-reducing headphones
contain a microphone that detects unwanted noise from the environment. A circuit then creates a sound wave that is an inverted version of the
noise wave, with peaks where the noise has troughs, and vice-versa. When this wave is played through the headphones, it destructively
interferes with the unwanted ambient noise. The same technique is used to reduce the noise from fans in commercial heating and ventilation
systems.
Superposition of waves
Combined wave = sum of waves
Add wave displacements at each pointPeak meets trough
Displacement is reduced