Non-coherent wave physics problem

  • Thread starter HarryWertM
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Hundreds, perhaps thousands, of wave generators [a floating buoy; a cable down to the lake bed; a motor rhythmically pulling and releasing the buoy] are placed in a limited section of a large, glass-smooth lake. The buoys are at random locations an average of a few wavelengths apart. The phases and frequencies of the generators are randomized, within some narrow frequency range. The question is: What wave pattern is observed at a large distance from the buoyed area?

I have no math to tackle this. My intuition says that very small choppy waves will be observed. The wavelengths of the "small" waves will be much shorter than the generating buoy waves, and highly variable. I do not know if any "quantization" effects would be involved. I am wondering if there might be some kind of very long-length "standing wave" formed around the buoy area.
 
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AFIK thi scenario is a large scale phenomenon where we would not use QM to solve wave shapes and forms. So a classical approach is justified here.
 

Delta2

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As i see it you just cant get waves with frequency much higher (or wave lengths much shorter) than those beloning in the narrow frequency range of the generators. Otherwise the fourier transform of the composite "small" wave forms would give non neglibible frequency components outside that narrow frequency range.
 

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