What happens when you add multiple sine functions?

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Discussion Overview

The discussion revolves around the addition of multiple sine functions, specifically exploring the mathematical behavior and graphical representation of sums like y=sin(x) + sin(2x) and more complex combinations involving multiple sine terms with phase shifts. The scope includes theoretical exploration and graphical interpretation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants inquire about the implications of adding two sine functions, questioning what happens to properties like amplitude and period.
  • Others suggest that drawing the graph is a useful way to visualize the result of adding sine functions.
  • One participant presents a formula for the sum of two sine functions, indicating a potential method for simplification.
  • Some participants argue that the resulting function from adding multiple sine functions is no longer a simple sinusoid, complicating the discussion of amplitude and phase shift.
  • There are suggestions to experiment with different combinations of sine functions to observe the resulting shapes.

Areas of Agreement / Disagreement

Participants express differing views on whether the sum of sine functions can be simplified or characterized in the same way as individual sine functions. There is no consensus on a universal answer regarding the properties of the resulting functions.

Contextual Notes

Some limitations include the dependence on definitions of amplitude and phase shift, which may not apply in the same way to the sums of multiple sine functions as they do to pure sinusoids.

Who May Find This Useful

This discussion may be of interest to individuals exploring wave functions, mathematical properties of trigonometric functions, or those looking to deepen their understanding of periodic phenomena in mathematics.

forumuser420
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What happens when you add two sin functions for example:
y=sin(x) + sin(2x)

***additional questions***
how about adding more than two funtions such as
y=sin(x+p/2)+sin(2x+p/2)+sin(3x+p/2)+sin(4x+p/2)+sin(5x+p/2)+sin(6x+p/2)+sin(7x+p/2)
 
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What do you mean what happens? You get the sum. Draw the graph and have a look. It looks cool.

Do you mean, can you reduce the answer in some neat way? I don't think so, but I could be wrong.
 
phinds said:
What do you mean what happens? You get the sum. Draw the graph and have a look. It looks cool.

Do you mean, can you reduce the answer in some neat way? I don't think so, but I could be wrong.


As in what happens to the amplitude, period, phase shift etc,
 
Jeez, guy ... if you can't see in your head what it does, draw the graph and it will become obvious what it does.
 
This may help:

sin(a)+sin(b)=2(sin(.5)(a+b) X cos (.5)(a-b))
 
I don't think you can get some universal answer for this, because your sum is a new function which is not a simple sinusoid anymore, although it is periodic. So it doesn't make sense to speak of an amplitude or a phase shift, at least not in the same sense as in with pure sinusoids.

This is your function (y = sinx + sin2x)
banAP.png
 
Lajka said:
I don't think you can get some universal answer for this, because your sum is a new function which is not a simple sinusoid anymore, although it is periodic. So it doesn't make sense to speak of an amplitude or a phase shift, at least not in the same sense as in with pure sinusoids.

This is your function (y = sinx + sin2x)
banAP.png

Yeah, that's what I was trying to get HIM to do. How's he going to learn if you do it for him?
 
If you want to have a bit of fun, try adding sin(x) + sin(2x)/2 + sin(3x)/3 and so on, and see what shape you get.
 
phinds said:
Yeah, that's what I was trying to get HIM to do. How's he going to learn if you do it for him?

Ah, sorry, didn't realize you were trying to educate him that way. Let's hope he'll still learn, tho.
 
  • #10
thx for help everyone...hopefully i will be able to return the favour sometime in the near future... I am new to the site and atm it is mostly welcoming so once again thanks :)
 

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