  We present a mechanism for the formation of the low frequency 1/f magnetic
spectrum based on numerical solutions of a shell reduced-MHD model of the
turbulent dynamics inside the sub-Alfv\'enic solar wind. We assign reasonably
realistic profiles to the wind speed and the density along the radial
direction, and a radial magnetic field. Alfv\'en waves of short periodicity
(600 s) are injected at the base of the chromosphere, penetrate into the corona
and are partially reflected, thus triggering a turbulent cascade. The cascade
is strong for the reflected wave while it is weak for the outward propagating
waves. Reflection at the transition region recycles the strong turbulent
spectrum into the outward weak spectrum, which is advected beyond the
Alfv\'enic critical point without substantial evolution. There, the magnetic
field has a perpendicular power-law spectrum with slope close to the Kolmogorov
-5/3. The parallel spectrum is inherited from the frequency spectrum of large
(perpendicular) eddies. The shape is a double power-law with slopes of -1 and
-2 at low and high frequencies respectively, the position of the break
depending on the injected spectrum. We suggest that the double power-law
spectrum measured by Helios at 0.3 AU, where the average magnetic field is not
aligned with the radial (contrary to our assumptions) results from the
combination of such different spectral slopes. At low frequency the parallel
spectrum dominates with its characteristic 1/f shape, while at higher
frequencies its steep spectral slope (-2) is masked by the more energetic
perpendicular spectrum (slope -5/3).
