  We have studied the $1/f$ voltage noise of gold nano-contacts in
electromigrated and mechanically controlled break-junctions having resistance
values $R$ that can be tuned from 10 $\Omega$ (many channels) to 10 k$\Omega$
(single atom contact). The noise is caused by resistance fluctuations as
evidenced by the $S_V\propto V^2$ dependence of the power spectral density
$S_V$ on the applied DC voltage $V$. As a function of $R$ the normalized noise
$S_V/V^2$ shows a pronounced cross-over from $\propto R^3$ for low-ohmic
junctions to $\propto R^{1.5}$ for high-ohmic ones. The measured powers of 3
and 1.5 are in agreement with $1/f$-noise generated in the bulk and reflect the
transition from diffusive to ballistic transport.
