Understanding Period and Frequency in Composite Sine Functions

[Cluelessness]

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

 

[DonAntonio]

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

 

[Cluelessness]

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?

 

[nucl34rgg]

It would appear you are searching for this:
http://en.wikipedia.org/wiki/Fourier_series
:)

 

[CellCoree]

Hi there! Great question. When adding two sine functions, the period and frequency of the resulting composite function will depend on the specific frequencies and phases of the individual sine functions being added. If the two frequencies are the same, the resulting function will have the same period and frequency as the individual functions. However, if the frequencies are different, the resulting function will have a new frequency that is the sum of the two individual frequencies. The period of the resulting function will also change accordingly. It is important to note that the phases of the individual functions can also affect the resulting function, so it is important to consider all factors when adding composite sine functions. I hope this helps!