Complex wave creation I'm wondering about the creation of complex waves. For example if I had an infinitely long piece of rope and a mechanism to add energy to it in constantly varying ways so it became an incredibly long and complex wave. Do physicists regard all variances as different waves (breaking the energies down into smaller measurements) or would the entirety be regarded as a "complex wave" (a single unit)? 
Note: I came to think of this after reading about neutrino oscillations and also thought that waves created in the early universe that have yet to interact with anything could be very detailed. Also a wave-function is said to include all possibilities for movement.  
 A: A complicated waveform is not a "single unit"; it can in principle be mathematically "taken apart" or separated out into a list of different individual fundamental frequencies whose sum yields back the original complex waveform. The mathematical tool used to decompose complicated signals or waveforms into their constituent frequencies is called Fourier analysis. 
A: Re. 

Do physicists regard all variances as different waves (breaking the
  energies down into smaller measurements) or would the entirety be
  regarded as a "complex wave" (a single unit)?

Either approach could be used depending on the situation.  Many times breaking the wave into simpler wave components is preferred.
For a simple example: if the wave is given by $f(x-ct)+g(x-ct)$ and if the system is linear, each wave, $f(x-ct)$ and $g(x-ct)$ can be considered separately.  This does not have to done in the frequency domain (Fourier analysis) but instead can be done in the time-space domain without considering each frequency component separately.  This can be useful for non periodic waves and especially short non repeating pulses.
