High School Add two functions, same frequency to produce one greater?

[grahas]

Is their any way to add two wave functions like sin or cos in such a way that you could double the frequency or at least increase it?

 

[jedishrfu]

I don't see how but what if you multiply them?

You could use the desmos calculator online to plot some examples:

https://www.desmos.com/calculator

 

[mfb]

You can follow the definition of a frequency to see that every sum of functions of the same frequency has the same frequency again.

 

[grahas]

^That was my personal conclusions as well. I ask because I was wondering if their was a way to increase the frequency of the E&M waves by combining them some how.

 

[mfb]

Well, you can play some tricks.

Define f(x)=sin(x) for [0,pi], [2pi,3pi], [4pi, 5pi] and so on, f(x)=0 otherwise.
Define g(x)=-sin(x) for [pi,2pi], [3pi,4pi], [5pi, 6pi] and so on, g(x)=0 otherwise.
Both functions have a period of 2 pi.
Define h(x) = f(x)+g(x) = |sin(x)| which has a period of pi as h(x+pi)=h(x) for all x. It also has a period of 2 pi as h(x+2pi)=h(x) for all x.

To analyze this properly, you can use Fourier transformations of the functions. They add nicely - a frequency component that is present in the sum has to be present in at least one of the summed functions. This is also true for electromagnetic waves, you cannot create higher frequencies simply by having two beams illuminate the same place.

In matter, there are exotic effects which can lead to higher electromagnetic frequencies. This is known as upconversion.

 

[jbriggs444]

Is their any way to add two wave functions like sin or cos in such a way that you could double the frequency or at least increase it?

You could take +sin x and -sin x. Upon adding them you would have a function with every frequency.

 

[grahas]

Thanks for the replies, they are really great.

 

[WWGD]

If the ratio of the periods is Rational, then the sum of periodic functions is periodic with period the "LCM" .