I’m studying engineering, and I see sine waves everywhere I look. why is this waveform so common in nature?
In: Mathematics
Wave phenomenon appear all the time in nature but I’d disagree sinusoids in particular are showing up a lot. What distinguishes sinusoids from other waves is their mathematical convenience, being tied to a simple, linear differential equation and exponentiation with complex numbers. That mathematical convenience means we’re often expressing non-sinusoidal waves as sums of sinusoids or outright approximating a non-sinusoid with a sinusoid, often via simplifying assumptions.
For instance, a pendulum swing isn’t actually a sine wave, it’s just common practice to take the ODE governing a pendulum’s motion, which has no explicit solution in elementary functions, and literally replace it with another ODE that has a sine wave solution, justifying it by saying something about a small angle approximation. To catalog the pendulum’s swing as a natural occurrence of a sine wave is to not critically examine the simplifying steps we took in our analysis.
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