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which one do you use when and why? It is possible to use both: $$x(t)=A\cos(\omega t)+B\sin(\omega t)$$ or either, as Simon Bridge suggests in his answer, or neither (explicitly) by using complex exponential forms: $$z(t) = Ce^{i\omega t}+De^{-i\omega t}$$ Which one to use is up to you. They all are correct and all will work. One of them is usually ...


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There are two ways to describe a sound wave. One is in terms of displacement of the medium and the other is in terms of pressure. This simple diagram shows that tthe two descriptions are $90^\circ$ out of phase with one another. Note that at a compression $C$ where the pressure is a maximum the displacement of the particle is zero and the same is true ...


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These curves show acoustic displacement or acoustic velocity. For acoustic pressure they would be "inverted" (nodes at the open end, antinodes at the closed end). In presented 1D case are all of them actually scalars (or can be treated as such). The curves show just the magnitude. I know, these graphics are confusing. Nowadays it could be easily done by ...


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Sound waves are made of alternation of compression (higher density) and rarefaction (lower density) regions in the air. However, this can be somewhat difficult to visualize. Because of this, textbooks often show the wave like it's a string in the organ pipe. Really what the curves are showing you in the amplitude of this compression wave. It's also drawn ...


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A few observations. First - if you record sound for a short time, the bandwidth of the sample will result in a smearing of the peaks. This only really matters if the sample is very short - with a 1 second sample you would have 1 Hz resolution, but if you sample for 0.01 second, the bandwidth is 100 Hz. Second, you are using a scale that is quite compressed ...


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Imagine a little wheel spinning on the rim of a big wheel. The resulting motion of a point on the little wheel is a combination of different simple harmonic motions. Think $$x = A\sin(\omega_1 t + \phi_1) + B \sin(\omega_2 t + \phi_2)$$ Depending on the relative frequencies and phases, the max amplitude can be $A+B$; the kinetic energy is just $\frac12 m ...



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