to a completeness limit of 1 mJy and a further 12 deg$^2$ to a completeness limit of 0.5 mJy. The 10C survey therefore provides the ideal starting point from which to study the faint, high-frequency sky. This survey has recently been extended to even fainter flux densities in two of the 10C fields by Whittam et al. (in prep), who calculated the 15 GHz source counts down to 0.1 mJy.

To investigate the nature of the extragalactic radio source population multi-wavelength studies are required, as the power-law nature of radio spectra means that radio data alone is not sufficient to classify source types or estimate redshifts. In the first paper in this series studying the faint radio source population at 15.7 GHz (@2013MNRAS.429.2080W, hereafter Paper I) we discuss a sample of sources selected from the Lockman Hole for which data over a wide range of frequencies are available. The Lockman Hole is a region of the sky centred near 10$^{\rm h}$45$^{\rm m}$, +58$^{\circ}$ (J2000 coordinates, which are used throughout this work) with exceptionally low <span style="font-variant:small-caps;">Hi</span> column density [@1986ApJ...302..432L]. The low infrared background (0.38 MJy sr$^{-1}$ at 100 $\muup$m; @2003PASP..115..897L) in this area of the sky makes it ideal for 