Non-Sinusoidal Standing Waves Existence?

[QuantumCuriosity42]

TL;DR

Looking for evidence and visual demonstrations of non-sinusoidal standing waves.

Hi everyone,

I'm curious if standing waves must be sinusoidal or if they can also be non-sinusoidal. Can anyone point me to videos or simulations of non-sinusoidal standing waves in action?

Thanks!

 

[DaveE]

It's all about the boundary conditions for the DEs, like bessel function for circles, etc.

 

[QuantumCuriosity42]

It's all about the boundary conditions for the DEs, like bessel function for circles, etc.

Thanks, and what is the special boundary condition that works for sinusoids but not for other shapes?

 

[berkeman]

Thanks, and what is the special boundary condition that works for sinusoids but not for other shapes?

Are you familiar with Fourier analysis? When you say non-sinusoidal waveforms, what exactly do you mean?

 

[QuantumCuriosity42]

Are you familiar with Fourier analysis? When you say non-sinusoidal waveforms, what exactly do you mean?

Yes I am. I mean any other shape, like a square or triangular wave, which also is a standing wave.

 

[berkeman]

Yes I am. I mean any other shape, like a square or triangular wave, which also is a standing wave.

But those are composed of sinusoidal waves, no?

 

[QuantumCuriosity42]

But those are composed of sinusoidal waves, no?

Yes, but can multiple sinusoidal waves be stationary at the same time under the same boundary conditions?

 

[DaveE]

Typically standing waves occur at a system's resonant frequencies. Those natural responses can be excited by any driving function that contains that frequency. It doesn't have to be just one. Think of a violin string that is aggressively bowed (is that a verb?), it can have multiple harmonics excited as standing waves. But it doesn't sound, or look like a pure sine wave. Which leads us back to @berkeman's question about fourier transforms, and what you really mean by "non-sinusoidal".

 

[berkeman]

aggressively bowed (is that a verb?)

Yes it is, although technically it is a verb phrase; it's a verb modified by an adverb.

 

[Vanadium 50]

We have three threads on this. OP, are you going to keep asking again and again and again and again and again until you get the answer you want? Maybe if you tell us what this is all about we could provide a more satisfactory response.

 

[berkeman]

Well yeah, there's that. Thread closed for Moderation...

 

[berkeman]

Thread is reopened provisionally.

@QuantumCuriosity42 -- Why are you asking this type of question (repeatedly)? If you understand Fourier Analysis, you should be able to answer this question for yourself.