Add two functions, same frequency to produce one greater?

In summary, there is no way to double or increase the frequency of two wave functions like sin or cos by simply adding them together. However, there are certain tricks and special cases, such as using the desmos calculator or defining functions with specific periods, that can result in a sum with a higher frequency. In matter, there are also exotic effects that can lead to higher electromagnetic frequencies. Overall, the sum of periodic functions will have a frequency that is present in at least one of the summed functions.
  • #1
grahas
32
1
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?
 
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  • #3
You can follow the definition of a frequency to see that every sum of functions of the same frequency has the same frequency again.
 
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Likes jedishrfu
  • #4
^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.
 
  • #5
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.
 
  • #6
grahas said:
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.
 
  • #7
Thanks for the replies, they are really great.
 
  • #8
If the ratio of the periods is Rational, then the sum of periodic functions is periodic with period the "LCM" .
 

1. What does it mean to add two functions with the same frequency?

Adding two functions with the same frequency means to combine two mathematical functions that have the same rate of oscillation or repetition. This can be thought of as adding two waves with the same wavelength and amplitude.

2. Can two functions with different frequencies be added?

Yes, two functions with different frequencies can be added. The resulting function will have a new frequency that is the sum of the two original frequencies. This is similar to adding two waves with different wavelengths and amplitudes.

3. What happens to the amplitude when adding two functions with the same frequency?

When adding two functions with the same frequency, the resulting amplitude will be the sum of the two original amplitudes. This means that the new function will have a larger amplitude than either of the original functions.

4. Is there a limit to the frequencies that can be added together?

No, there is no limit to the frequencies that can be added together. However, as the frequencies become larger, the resulting function may become more complex and difficult to analyze.

5. How is adding two functions with the same frequency useful in scientific research?

Adding two functions with the same frequency can be useful in a variety of scientific research areas, such as signal processing, acoustics, and electromagnetic theory. It allows for the combination of different signals or waves, which can provide insights and solutions to complex problems.

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