Since a wavelength, $\lambda$, is the length of a entire cycle
How many $\lambda$ (complete cycles) can a composed wave have? I mean, for $n \lambda$, how big can $n$ be? And what does it mean, physically?
I'm not necessarily talking about an electromagnetic wave, it can be an 'electron wave' since particles can be interpreted as waves.
The mathematical wave you are showing , has no limit of length it can go from minus infinity to plus infinity,
When a mathematical wave function is used to fit specific physical behavior, as waves of water and sound, it will depend on the particular boundary conditions of the case under study,and more than one function will be needed.
For the case of the laser, which has a fixed wavelength within error, the length it can travel will depend on the energy available before the wave turns into the photons that compose it, because all laser beams have a divergence with distance . Photons are not a wave, so that will be the end of the laser beam.
A single photon would represent a "cycle", in a laser we have stimulated emission which means a single photon passes by an excited atom and induces another identical photon instantaneously.
Photons are always created one at a time by electrons in atoms .... and photons are always absorbed one at a time. In the laser cavity we have unique constant sinusoidal EM field ... you can think of photons jumping into this field ... this gives a lot of synchronicity to the emitted single photons.
A material wave can go on as long as you want.
