What happens when you add multiple sine functions?

In summary, when adding two sin functions, you get the sum of the functions and the resulting graph can look visually appealing. Adding more than two sin functions can result in a new function that is not a simple sinusoid and therefore cannot be described by traditional parameters such as amplitude or phase shift. To understand the effects of adding multiple sin functions, it is recommended to draw the graph and observe the shape.
  • #1
forumuser420
3
0
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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  • #2
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.
 
  • #3
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,
 
  • #4
Jeez, guy ... if you can't see in your head what it does, draw the graph and it will become obvious what it does.
 
  • #5
This may help:

sin(a)+sin(b)=2(sin(.5)(a+b) X cos (.5)(a-b))
 
  • #6
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
 
  • #7
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?
 
  • #8
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.
 
  • #9
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 :)
 

FAQ: What happens when you add multiple sine functions?

What is the formula for adding sine functions?

The formula for adding two sine functions is:
f(x) = a sin(bx + c) + d
where a and b are the amplitude and frequency, respectively, of the sine functions, c is the phase shift, and d is the vertical shift.

Is it possible to add more than two sine functions?

Yes, it is possible to add more than two sine functions. The formula for adding three or more sine functions is the same as adding two functions, but you would simply add more terms to the equation.

How do I determine the amplitude and frequency of the resulting sine function after adding two or more sine functions?

To determine the amplitude and frequency of the resulting sine function, you can use the properties of trigonometric functions. The amplitude will be the sum of the individual amplitudes of the sine functions, while the frequency will be the least common multiple of the individual frequencies.

Can I add sine functions with different periods?

Yes, you can add sine functions with different periods. The resulting function will have a period that is the least common multiple of the individual periods.

Are there any special cases when adding sine functions?

Yes, there are two special cases to consider when adding sine functions. If the two functions have the same amplitude, frequency, and phase shift, then the resulting function will have a larger amplitude. If the two functions have opposite phases (c and -c), then the resulting function will have a vertical shift of 0.

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