Will changing the amplitude change the frequency of a wave, or is it possible for a specific frequency (50 Hz. for example) to generate from shifting amplitude patterns?
It's completely possible to change the amplitude (the difference between the maximun value of the wave and the minimun) without changing the frecuency.
Think this in AC, where you can have signals with different voltage but the same frecuency.
To illustrate it I'll show you this for a harmonic wave: $$x(t)=Acos(\omega t+\phi)$$ You can vary the amplitude (for example, adding another wave of the same frecuency and phase) and the resulting wave will be just: $$x'(t)=A'cos(\omega t+\phi)$$
Note that if we add two waves, in general, the new frecuency does not need to be the same.