![]() ![]() Displacement refers to the “height” of the wave above the x-axis and position refers to the location in the medium where you measured the displacement. At each location in the medium, the pulse/wave has a different “height.” In math-speak, displacement is a function of position. The key insight is recognizing that pulses/waves cannot be described by a single number for height. ![]() Does the principle of superposition still apply? The short answer is “yes.” This popsicle sticks video (0:39 youTube) shows how. Intuition also suggests that exact answer depends on the shapes of the two pulses and how they line up. But what happens when if the two pulses don’t align perfectly? Intuition suggests the result won’t be a single peak- the combined shape will probably retain some of the features of the two individual pulses but the combined shape will be taller that either pulse alone. Is it possible for two sounds to combine to make a sound that’s quieter than either sound alone? Is it possible to add two sounds together to create silence? A closer look at the mathĪt the exact moment a crest 3 units tall perfectly aligns a crest 1 unit tall, the result is a crest that’s 4 units tall. (Think of troughs as having negative height). When a crest 3 units tall meets meets a trough 1 unit deep, the pulse is 2 units tall. At the exact moment a pulse with a crest 3 units tall meets meets pulse with a crest 1 unit tall, the pulse is temporarily 4 units tall. No matter whether it’s constructive or destructive interference, the math is addition. Once the waves/pulses travel pass each other, they reemerge as if nothing had happened! Destructive interference: When the pulses meet, the heights still add (but one height is negative). Notice that the interference only occurs while the two waves overlap. If crest meets trough, the result is a smaller pulse/wave- this is called destructive interference. Constructive interference: When two pulses meet, the heights add. If two crests (or two troughs) line up, the result is a pulse/wave that’s larger than either crest (trough) alone- this is called constructive interference. Where two (or more) waves (or pulses) overlap, the displacements of the resulting wave (or pulse) is equal to the sum of the displacements each wave (or pulse) would have if it was at the location alone. The basic rule that governs interference is the principle of superposition: Where and when waves overlap, the waves combine to form a single wave. After the waves meet, they return to their original “selves” and continue on as if they had never interacted at all. Unlike particles, waves can and do pass through each other. Interference 33 Principle of superposition Interference and the principle of superposition
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