![]() But many of these factors are very minor, and can be reasonably ignored in most circumstances. Real systems are often complicated, often messy, and depend on an extremely large number of factors. Don’t all sound waves cause a change in acoustic pressure? And if that’s true, then shouldn’t all sound waves change the speed of sound, and thus act non-linearly? And while that may be true, that brings us to the concept of approximation, linearization, and how science often bends (or rather straightens) the truth to make things simpler, giving us more elegant and useful solutions.Īpproximation is one of science’s favorite tools. If you read that last sentence carefully, you might notice something fishy. ![]() ![]() The shockwaves from an explosion or supersonic object are so extreme that they behave differently than less intense sounds.” Photo credit Gary Settles/Penn State This is because sound speed is a function of pressure, so as acoustic pressure increases, so does the speed of the wave. So if I took two identical shock waves, and added them together, the resulting shockwave would move faster than either of those shock waves alone. For example, the more powerful the shock wave is, the faster it moves. These powerful waves often occur with an explosion, and are also generated when something breaks the speed of sound (a so-called “ Sonic Boom.”) Shock waves are acoustic waves, but they certainly aren’t linear. This is called non-linearity, and it also has its place in acoustics. Unfortunately, not everything is linear, and sometimes superposition doesn’t work. Because of superposition, scientists can find an answer, and keep using that same answer over and over again without having to worry that it’s changed. We regularly take complicated problems with lots of sound sources at different levels in different locations, and make the problems easier by breaking them up and solving them piece by piece. Acoustic impedance can give a full description of the behavior of a linear system, using superposition. The reason why normal modes are so fundamental is that the modes, which are just solutions to the equations of motion of the system, can be added together to find all new solutions. Ever wonder how to generate these interesting looking interference patterns? Thanks to linearity and superposition, the answer is as simple as 1+1.īecause all of these systems are linear, scientists make regular use of superposition.
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