Introduction to Fourier Series - Adding Sine Waves to make Sawtooth, Square, and Triangle Waves
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- Опубліковано 25 сер 2024
- We look at special functions that can be created by adding sine waves together. Algebra 2 students who have learned about the amplitude and period of graphed sine waves can begin to understand a bit about wave superposition and Fourier series by playing around a bit with Desmos and copying some of the patterns shown in the video. 1:15 Sawtooth Wave 3:00 Square Wave 4:25 Triangle Wave.
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Terrific! You chose an interesting topic. I'll bet people learned some good stuff from your presentation.
is the last sound wave type and the last maths calculus equation to do with creating a triangle wave ?
They don't know what they are missing. I subscribed before i got to the end. You know after 10 long years! I will finish all of yours without a break. You are a techer par excellence. Could you please expand it to explain how this series takes the shape of some very complicated image?🙏🙏🙏
Thank you. That's a great idea. I'll try to find time to build up how to calculate them for some different shapes. In the meantime, the channel "Smarter Every Day" has a beautiful video on Fourier series.
Why use for example sin(πnx) instead of sin(nx), why is the π needed?
Just for style. I like it because a generic sine wave can be written as A sin ( [2pi/T ]x) or A sin( [2pi f] x) in which T is the period or f is the frequency (# of cycles per horizontal unit). Indeed,, you definitely don't have to do it the way I chose to.
Even & Odd = sawtooth
Odd = square
Even = ??
Is the program in the video available ?
It's just the Desmos graphing calculator. A Google search will pull it up pretty quickly.
@@dr.piercesphysicsmath9071 brilliant thank you for getting back to me. Great video helped a lot.