  The current noise of a voltage biased interacting quantum wire adiabatically
connected to metallic leads is computed in presence of an impurity in the wire.
We find that in the weak backscattering limit the Fano factor characterizing
the ratio between shot noise and backscattering current crucially depends on
the noise frequency relative to the ballistic frequency v_F/gL, where v_F is
the Fermi velocity, g the Luttinger liquid interaction parameter, and L the
length of the wire. In contrast to chiral Luttinger liquids, the noise is not
only due to the Poissonian backscattering of fractionally charged
quasiparticles at the impurity, but also depends on Andreev-type reflections of
plasmons at the contacts, so that the frequency dependence of the noise needs
to be analyzed to extract the fractional charge e*=e g of the bulk excitations.
We show that the frequencies needed to see interaction effects in the Fano
factor are within experimental reach.
