Are All Waves Sinusoidal, or Are There Non-Sinusoidal Waveforms?

[jmatejka]

I have experience with wave mechanics from a undergrad perspective, Modern Physics, etc.

I saw the statement the other day, "All waveforms are sinusoidal". I believe this to be not 100% correct.

Texts usually show a "nice" looking sine wave for most things "wave". I believe this is the starting point, for something that is usually more complex.

In the most simple terms, the up and down motion of any wave could be called "sinusoidal" correct?

From EE, I am aware of artificailly generated, Square, Triangle and Sawtooth Waveforms.

Would you say "most" waves, light, water, or otherwise are sine with added "harmonics" or funcitons?



Wiki seems to say there "IS" non-sinusoidal waves:

"Examples of non-sinusoidal waveforms include square waves, rectangular waves, ramp waves, triangle waves, spiked waves and sawtooth waves."

http://en.wikipedia.org/wiki/Non-sinusoidal_waveform

Would you call these "piecework" function waves?


Any "naturally occurring" examples of non-sinusoidal waves?

Impossible for light waves to be non-sinusoidal, correct?

 

[nonequilibrium]

Well I think you'd only create a sinusoidal wave in a taut string if you're moving your hand like a harmonic oscillator; for example instead of moving it as such, pause your hand for a few seconds every time you're at the "top": I don't think you'll see a sinusoidal wave anymore. (I'm seeing something in my head which looks like a sinusoidal wave with at each positive extremum a piece of a straight line copy-pasted into it.)

 

[jmatejka]

Well I think you'd only create a sinusoidal wave in a taut string if you're moving your hand like a harmonic oscillator; for example instead of moving it as such, pause your hand for a few seconds every time you're at the "top": I don't think you'll see a sinusoidal wave anymore. (I'm seeing something in my head which looks like a sinusoidal wave with at each positive extremum a piece of a straight line copy-pasted into it.)

At the point your hand stops moving, would it become like a guitar string, still sinusoidal with nodes?

 

[nonequilibrium]

Here is a picture of the string:

 

[arildno]

"I have experience with wave mechanics from a undergrad perspective, Modern Physics, etc.

I saw the statement the other day, "All waveforms are sinusoidal". I believe this to be not 100% correct.
"

Yes and no.

Why it is a totally incorrect statement:
If it was meant by "sinusoidal" that the every wave can be represented by a single sinus function, then it is wrong. It is also wrong that every wave phenomenon can be written as a finite sum of cosine and sine waves.

However:
The set of sines and cosines form a mathematically complete set of functions, so that any function is representable by a, usually, infinite series of sines&cosines.

This, however, cannot defend the use of "sinusoidal" as descriptive of wave shapes in general, then we could equally well call all waves, say, "polynomial", since the polynomials also represent a mathematically complete set of functions.

Thus, I agree with you, although I'd say the statement is 0% correct, rather than "not quite 100%" correct.

 

[Niznar]

It's somewhat true.

If you've taken courses in signal analysis you might be aware of Fourier Analysis, which is a topic in mathematics where you can represent general functions in terms of sums of trigonometric functions.

If you look at a square wave, for instance, you can visually create that wave by adding phase and amplitude shifted sine waves together, widening the troughs and flattening the peaks in the wave.

 

[jmatejka]

"I have experience with wave mechanics from a undergrad perspective, Modern Physics, etc.

I saw the statement the other day, "All waveforms are sinusoidal". I believe this to be not 100% correct.
"

Yes and no.

Why it is a totally incorrect statement:
If it was meant by "sinusoidal" that the every wave can be represented by a single sinus function, then it is wrong. It is also wrong that every wave phenomenon can be written as a finite sum of cosine and sine waves.

However:
The set of sines and cosines form a mathematically complete set of functions, so that any function is representable by a, usually, infinite series of sines&cosines.

This, however, cannot defend the use of "sinusoidal" as descriptive of wave shapes in general, then we could equally well call all waves, say, "polynomial", since the polynomials also represent a mathematically complete set of functions.

Thus, I agree with you, although I'd say the statement is 0% correct, rather than "not quite 100%" correct.

Thanks, agreed.

I have been looking at some "funcitons for Non-Sinusoidal waveforms:, here:

http://www.elect.mrt.ac.lk/EE201_non_sinusoidal_part_1.pdf

Although, "Non-Sinusoidal", they have Sin or Cos in their function to achieve Periodicity where applicable.

Sooooo, if the Sin/Cos part of the function is used only for Periodicity, the "wave itself", can still be Non-Sinusoidal, Correct?

 

[jmatejka]

Here is a picture of the string:

Thanks for the pic!

 

[jmatejka]

It's somewhat true.

If you've taken courses in signal analysis you might be aware of Fourier Analysis, which is a topic in mathematics where you can represent general functions in terms of sums of trigonometric functions.

If you look at a square wave, for instance, you can visually create that wave by adding phase and amplitude shifted sine waves together, widening the troughs and flattening the peaks in the wave.

Create the Non-Sinusoidal function from modified Sinusoidal functions, interesting. Thanks!

Almost a semantics game at somepoint maybe?