waves - Using the equations $y(x,t)=Asin(kx-wt)$ and $w=2pi f$, if we solve for amplitude could we determine a relationship between amplitude and frequency?

I'm reading all over the internet that there is no relationship between frequency and amplitude of a wave given the context of a simple experiment where a string is tied between two points and one of the points is made to oscillate with some frequency $f$. However, if we solve the first equation for amplitude we see that

$$ \frac {y(x,t)}{\sin(kx-wt)} = A $$

And knowing that $w = 2\pi f$, couldn't we say that there is at least some sort of relationship between amplitude and frequency?