- #26

Saw

Gold Member

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No... I am not trying to do this. Don't be misled by the title of the thread. I am not trying to put energy into one mode and hopefully feel the effect in another. Since many posts ago, I re-formulated the question. I am just superposing waves. First, I combined two waves of different frequencies (f1 and f2) and I want to combine them with a third wave of another frequency (f1 - f2) and observe the outcome.What are you doing to one mode by trying to add energy to anotherorthogonalmode? By definition of what orthogonal means, the two modes cannot affect each other in a linear system.

That is another thing, whether the third wave will find "resonance" in the system over which it will be superposed. Maybe not, but before deciding, please consider these comments on the description of the system.If you try to impress a periodic 'force' on the system that is not at one of the resonant frequencies you can get two results - if this exciter frequency is lower than the resonance frequencies then the whole system will move by the small displacement of the exciter, if the exciting frequency is higher then there will be no resulting movement. See the graph in this link which is only worth describing with a finite value of Q.

The combined wave is a “beat wave”. Look at its math description in Wikipedia:The mathematical description is A+B with no hint of C X D.

$$\cos (2\pi {f_1}t) + \cos (2\pi {f_2}t) = 2\cos \left( {2\pi \frac{{{f_1} + {f_2}}}{2}t} \right)\cos \left( {2\pi \frac{{{f_1} - {f_2}}}{2}t} \right)$$

The sum of waves A (f1) and B (f2) is equivalent to the product of two other waves: C = a (fast) combined “beat wave” oscillating at the average frequency [f2 + f1)/2] and D = a (slow) wave oscillating at (f1 – f2), the rate of change of the amplitude of the said “beat wave”.

According to Wiki, “It can be said that the lower frequency cosine term is anIt is NOT a modulated wave.

*envelope*for the higher frequency one, ie that its amplitude is modulated”