Does sinusoidal play a role in physics?

[Gerenuk]

That is the essence of the fallacy "begging the question". Sorry that you think it is unhelpful to identify errors in logic.

I tell you what the error is. You believe that it must be completely certain that you can answer this (or even any?) question. Here however it is more appropriate to make suggestions and ask if these are going into the right direction. Or maybe suggesting an alternative formulation. Or asking specific questions about how I could have meant something - I might answer or maybe not know. This is a discussion process where both parties cooperate instead of fighting aggressively for the most judicially correct answer. To sum up, "yes" and "no" are sometimes premature. Cooperative discussions might not be the preferred style of all participants however.

 

[espen180]

The way you are describing the problem sounds more like a philisophical problem than a scientific question. In short, a good scientific question is one that is unambigous. This is clearly not the case here.

 

[Gerenuk]

The way you are describing the problem sounds more like a philisophical problem than a scientific question. In short, a good scientific question is one that is unambigous. This is clearly not the case here.

You are right. This question isn't what you consider a "good scientific question". Likewise you probably would have thought that when Einstein asked by inertial mass and gravitational mass is the same, is rather philosophical. And I already explained to DaleSpam this isn't a "crystal clear question + best answer gets a price" thread.
Actually I can define the question better but physicists don't seem to understand when I write I'm looking for a process where given an arbitrary boundary condition, spatial sine waves appear.

 

[SystemTheory]

Re:

Does sinusoidal play a role in physics?

As worded, the logical and proper answer to this question is yes. An open ended discussion would revolve around this question: What role does sinusoidal play in physics?. Then right and wrong answers are up for debate.

I'm looking for a process where given an arbitrary boundary condition, spatial sine waves appear.

This is a more specific question for which I lack an anwser. I can write a general equation for a standing wave (with help from an old textbook, I don't recall pure math easily) and for a given system, I identify the boundary conditions to write a specific equation. So what do you mean by an arbitrary boundary condition? Whether or not the actual function fits the sine is a problem of measurement error ...

 

[Gerenuk]

Thanks for your answer SystemTheory.

This is a more specific question for which I lack an anwser. I can write a general equation for a standing wave (with help from an old textbook, I don't recall pure math easily) and for a given system, I identify the boundary conditions to write a specific equation. So what do you mean by an arbitrary boundary condition? Whether or not the actual function fits the sine is a problem of measurement error ...

Boundary conditions for a fixed string are indeed what I would consider natural. So that's a good start. However, many standing waves are possible and without special care they will intermix. Just as all string instruments sound differently due to their different overtones.

 

[SystemTheory]

In system and signal analysis it is often more convenient to work in the frequency domain. The center frequency of a signal is drawn as an impulse of specified amplitude. In the time domain it is a sine wave of known amplitude and frequency. I suppose the quantum theory emerged since these impulses appear as spectral lines, and you are looking for a physical process that can yield a continuous, rather than discrete, set of sine wave boundary conditions?

If there is a spread in the frequency (group delay), or harmonic frequencies in the system, then there is a frequency distribution rather than an impulse of given amplitude. Is it possible to use some other math function than a sine to transform between the frequency domain? You seem to answer yes but pure math is difficult for me so I rely on Fourier, Laplace, and the smart guys from history ...

 

[diazona]

Boundary conditions for a fixed string are indeed what I would consider natural. So that's a good start. However, many standing waves are possible and without special care they will intermix. Just as all string instruments sound differently due to their different overtones.

So let me get this straight... you're looking for a physical system described by some differential equation which allows only a single sine wave - not a superposition of multiple sine waves - as a solution, regardless of the boundary conditions of the equation?

That seems like a tall order. I wouldn't be surprised if no such thing exists. Perhaps even provably so.

 

[espen180]

He doesn't allow a superposition, yet every sine wave can be expressed methematically as a superposition of multiple sines.

 

[Gerenuk]

If there is a spread in the frequency (group delay), or harmonic frequencies in the system, then there is a frequency distribution rather than an impulse of given amplitude. Is it possible to use some other math function than a sine to transform between the frequency domain? You seem to answer yes but pure math is difficult for me so I rely on Fourier, Laplace, and the smart guys from history ...

That is not what I meant. Fourier transform is surely the easiest way to solve it, but nature is fine solving the differential equations with a brute force (numerical) method, so the sine in this case is only useful to us.

So let me get this straight... you're looking for a physical system described by some differential equation which allows only a single sine wave - not a superposition of multiple sine waves - as a solution, regardless of the boundary conditions of the equation?

That's a very good description. Actually, I don't restrict myself to differential equations only, but it can be any "physical law". But thinking about it more probably most of the physics is differential equations.

He doesn't allow a superposition, yet every sine wave can be expressed methematically as a superposition of multiple sines.

First, an sine wave cannot be represented by other sines, and second you should try to read the posts word by word, because you are mixing up the statements mentioned.
I didn't exactly say I don't allow superpositions. I said I only need a pure sine wave (no matter if that sine is a superposition of whatever). A vibrating string just never is a pure sine wave. That's why all instruments have a different sound.

Maybe the following is a good statement of my question: Can you simulate the whole world on a computer which doesn't know about the sine function (and doesn't try to replicate it).