If we doubt we have the right number for the speed of light or the length of a wavelength,
\(f=\cfrac{c}{\lambda}=\cfrac{8^2}{3}\pi=67.02\,Hz\)
there is no reason to believe that we have defined the length of a second correctly either.
What happens at \(67.02\,Hz\)? Only after we have this per second period defined, can we define \(\lambda\) and so \(c\).
The egg stops here...