RMS of square, sine and triangle waves

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Homework Help Overview

The discussion revolves around calculating the RMS (Root Mean Square) values for square, triangle, and sine waves. The original poster expresses difficulty with triangle waves, particularly in finding the integrals due to their squared forms being more complex compared to sine and square waves.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss different methods for calculating RMS values, including integration and the use of graphical representations. Questions arise about the integration of triangle waves and the use of piecewise functions.

Discussion Status

Some participants have provided guidance on using piecewise functions for triangle waves and have clarified the simplicity of integrating square waves by considering the area under the graph. There is an ongoing exploration of the best methods for these calculations, with no explicit consensus reached.

Contextual Notes

Participants mention the use of Fourier series expansions for triangle waves, which may not be relevant for the current problem. The original poster also references external resources that may introduce additional complexity.

Juan Pablo
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I'm trying to calculate the RMS for square, triangle and sine waves. I can easily do the integrtion for sine waves and for square waves by looking at the graphic and getting the areas. It doesn't seem as easy for triangle waves since its squared form looks much more complicated and I'm not really sure how to calculate the integrals. I appreciate any guidance.

Thanks in advance.
 
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Do you know how to integrate without graphs? I.e. integrating using the equation for the wave?
 
Yeah sure, but most of the expressions for triangle waves use strange functions and I'm not sure how I would find the antiderivative of the triangle wave.
 
The expressions for a triangle wave should just be a bunch of linear functions next to each other...which will turn into parabolic functions when you square them. What strange functions are you talking about?

For example, a triangle wave may be: y=x for 0<x<1; y=-x+2 for 1<x<3; etc.
 
I feel like an idiot. I didn't realize I could use a piecewise function. Thanks! In the case of the square wave should I just use the graph for the integral or is there a more elegant way to do it? By strange function I meant the ones here http://en.wikipedia.org/wiki/Triangle_wave
 
The function there is a Fourier series expansion of a triangle wave. It's useful for some applications, though not this one particularly. Just use the piecewise definition, it's much easier.

I don't see any reason for the square wave to do any more than look at the area underneath the graph. That is the simplest method, and integrating is doing the same thing.
 
Thanks again! You really cleared out everything.
 

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