# Non-Sinusoidal Standing Waves Existence?

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• QuantumCuriosity42
QuantumCuriosity42
TL;DR Summary
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!

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

QuantumCuriosity42
DaveE said:
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?

QuantumCuriosity42 said:
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?

berkeman said:
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.

QuantumCuriosity42 said:
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?

berkeman said:
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?

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".

DaveE said:
aggressively bowed (is that a verb?)
Yes it is, although technically it is a verb phrase; it's a verb modified by an adverb.

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.

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

@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.

## What are non-sinusoidal standing waves?

Non-sinusoidal standing waves are standing wave patterns that do not follow a simple sinusoidal shape. Unlike sinusoidal standing waves, which are characterized by smooth, periodic sine or cosine functions, non-sinusoidal standing waves can take on more complex forms, including square waves, triangular waves, or other irregular shapes.

## How do non-sinusoidal standing waves form?

Non-sinusoidal standing waves form when the boundary conditions and the excitation sources create wave patterns that do not conform to simple sine or cosine functions. This can occur in systems with nonlinear properties, complex geometries, or when the driving forces themselves are non-sinusoidal. The superposition of multiple harmonic components can also result in non-sinusoidal standing wave patterns.

## Where can non-sinusoidal standing waves be observed?

Non-sinusoidal standing waves can be observed in a variety of physical systems, including electrical circuits with non-linear components, mechanical structures with complex boundary conditions, and fluid dynamics where the flow patterns are influenced by non-linear forces. They are also seen in acoustics, optics, and other fields where wave phenomena play a crucial role.

## What are the practical applications of non-sinusoidal standing waves?

Non-sinusoidal standing waves have practical applications in many fields. In electrical engineering, they are used in the design of filters and signal processing circuits. In mechanical engineering, understanding these waves can help in the analysis of vibrations in complex structures. In acoustics, they are important for the design of musical instruments and soundproofing materials. Additionally, they have applications in medical imaging and materials science.

## How can non-sinusoidal standing waves be analyzed?

Non-sinusoidal standing waves can be analyzed using Fourier analysis, which decomposes complex waveforms into their sinusoidal components. Numerical methods, such as finite element analysis (FEA) and computational fluid dynamics (CFD), can also be employed to model and study these waves in complex systems. Experimental techniques, including laser Doppler vibrometry and high-speed imaging, can be used to visualize and measure non-sinusoidal standing waves in physical systems.

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