  We analyze the spectrum of electron density oscillations in an interacting
one-dimensional electron system with an impurity. The system's inhomogeneity is
characterized by different values of Fermi wave vectors $k_F=k_{L/R}$ on
left/right side of the scatterer, leading to a Landauer dipole formation. We
demonstrate, that while in the noninteracting system the Friedel oscillations
possess only one periodicity related to the local $k_F$, say $k_L$ on the left
side, the interplay of the interactions and the Landauer dipole generates an
additional peak in the spectrum of density oscillations at the counterpart
$k_R$. Being only present in correlated systems, the position and shape of this
spectral feature, which in coordinate space is observable as a beating pattern
in the Friedel oscillations, reveals many important details about the nature of
interactions. Thus it has a potential to become an investigation tool in
condensed matter physics.
