I have 3 sine waves that I am adding. Frequencies are 300, 500, and 1K hz. I know that the period is one over the freq and I have modeled this system in Matlab and have found the period to be 10ms.
I cannot just use 1/f because of the summed sines. How do I calculate, by hand, the frequency and period of multiple sine waves that are added together?
It’s been a while since I studied this, but I think the period of the summed wave is the highest common multiple of the periods of the individual waves.
Frequencies of 1k, 500 and 300 Hz lead to periods of 1/1000, 1/500 ans 1/300 seconds respectively. The highest common multiple of these is 1/100s. This is 10 ms so agrees with the answer you gave.
Let me know if I can be of further help.
Sounds reasonable, but I don’t understand why that would be the case. Can anyone explain how that works?
Hard to explain without drawing, but hear goes.
The period of a wave is the “length”, in this case amount of time that, it takes for a wave to repeat itself. If you are summing the waves then this happens the first time that a whole number of each wave ends at the same point; or when all three waves “start” at the same point and therefore the whole thing starts again.
ie if your wavelengths are x, y and z then at the lowest value of w such that ax + by + cz = w where a, b and c are positive integers.
This is the definition of the lowest common multiple of x, y and z
Hope that is understandable.
Argh! Here
You know that after one period, the wave will repeat. In order for the total wave to repeat, then all three tributary waves must be repeating as well. And this only happens after an integer number of periods for each of the waves. Docklands, I think you meant to write this (correct me if I’m wrong):
ax = by = cz = w
You’re dead right Achernar.
Is that a threat? 
No. It’s a promise.
Crystal clear. Thanks alot!
Crystal clear. Thanks alot!
And if the wavelengths are incommensurable, then the sum is not periodic at all. It is “almost periodic” (a very technical concept, but if you know what Bessel functions are, they are almost periodic). And in real life, where everything is only approximate, you can assume that over a sufficiently short interval, they are commensurable. But expect long-term drift.
[useless trivia from a smart alec]
Of course, if they weren’t sine waves, it’s possible they could repeat at the freq. calculated as above, but have a smaller period:
AAAAAA period=1
I won’t bother with [/], I always am.
How to find the period of two signals added for example:
if f= s1+s2 where s1 is a square wave of (+ -) 1 V, period √6 secs and s2 is a square wave of (+ -) 1 V, period 1/√6 secs.
Is this signal periodic if not why?
Can anyone let me know about some link where I can learn all the examples of such type.
As was pointed out about 10 years ago in this thread, it’s the least common multiple (LCM) of the periods of the components. Write the period of the second wave as (√6)/6 secs to calculations easier, and it becomes obvious that the LCM is √6 secs: the first period is exactly 6 times as long as the second period, so the first period is the LCM.
Is there any book i can refer to learn more.
Or at least it divides the LCM; the minimal period may be smaller.
Nevermind