Understanding Period and Frequency in Composite Sine Functions

AI Thread Summary
When adding two sine functions with different frequencies, the resulting function does not have a simple period; instead, it creates a complex waveform with a period determined by the least common multiple of the individual periods. The frequency of the combined function is not a straightforward addition, as it depends on the interaction of the two original frequencies. Understanding frequency in this context relates to the inverse of the period, which is linked to the function's argument. The trigonometric identity sin x + sin y = 2 sin((x+y)/2) cos((x-y)/2) can help analyze the combination. For further exploration of decomposing complex waveforms, Fourier series can provide valuable insights.
Cluelessness
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Hey all!
I have a question concerning the addition of 2 sine functions.
Could anyone point me to the right direction as to what happens to the period and frequency when two sine functions are added together?
Note: when adding, these two functions possesses two different frequencies.
Thanks in advance! :D
 
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Cluelessness said:
Hey all!
I have a question concerning the addition of 2 sine functions.
Could anyone point me to the right direction as to what happens to the period and frequency when two sine functions are added together?
Note: when adding, these two functions possesses two different frequencies.
Thanks in advance! :D



I know what period of a trigonometric function is, but I can't say the same of "frequency" though

this seems to be a term from physics related to the inverse of the function's argument times 2\pi ...

Anyway, we have the trigonometric identity \sin x+\sin y=2\sin \frac{x+y}{2}\cos\frac{x-y}{2} .

DonAntonio
 
Thanks DonAntonio :D
But do you happen to know any other relationships apart from Simpsons' or Werner's?
My dilemma is, given a graph, how would you figure out what it is made up of? i.e what sine functions were added to produce that graph?
I just need a hint - do you happen to know any thing else which could help me?
 

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