I've studied a bit of frequency analysis with FFT and optimal phase binning and was taught that we can represent any composite waveform as the sum of its component frequencies.
I understand the maths works and gives meaningful results that we can use for design or to solve problems, but does this mean that sine waves are a natural 'element', like particles are for matter but in the time domain (4th dimension) – something that occurs in nature? Or are they a mathematical construct that helps us interpret nature?
Do pure, single frequencies occur through natural phenomena or processes?
I was taught about tuning forks but (without having tested it) I assume they will produce some harmonics as the straight bars have more than one mode of vibration.
Then I thought about the rotation of the planets but they are not pure sinusoids either since the gravity of other planets affects their rotation.
Finally I thought about light, but only lasers have a single frequency and as far as I know they don't occur naturally.
I assume I'm not the first human asking this question. Are you aware of any academic work on this matter?
Best Answer
Since no phenomenon is completely periodic (nothing keeps repeating from minus infinity to infinity), you could say that sine waves never occur in nature. Still, they are a good approximation in many cases and that is usually enough to consider something physical.
I would even go further and say that it is reasonable that everything in physics is a mathematical construct that helps us interpret nature, but that would lead to the philosophical debate of what is nature an so on. After all, almost everything in physics breaks down or at least becomes problematic at some regime: the notion of particles in strongly-interacting theories, energy in general relativity, the notion of a sound wave at the atomic scale...