the Alfvén speed $a$ is much less than the sound speed $c$, the $p$-modes are effectively fast waves. But on passing through the equipartition layer $a=c$ they partially transmit as acoustic waves (now slow) and partially convert to magnetically dominated fast waves [@Cal06aa; @SchCal06aa; @Cal07aa], depending on the attack angle between the wave vector and the magnetic field. In sunspot umbrae, $a=c$ is typically situated several hundred kilometres below the surface, whilst in penumbrae it is around the surface [@MatSolLag04aa]. In the regions surrounding sunspots, $a=c$ may crudely be equated with the level of the magnetic canopy in the low atmosphere.

3.  The transmitted slow waves above $a=c$ are essentially field-guided acoustic waves. Unlike their non-magnetic cousins though, they may still propagate vertically at frequencies below the acoustic cutoff (around 5 mHz), provided $\omega>\omega_c\cos\theta$, where $\theta$ is the field inclination from the vertical [@BelLer77aa]; the so-called ‘magneto-acoustic portals’ [@JefMcIArm06aa]. This ramp effect has recently been shown computationally to be far more important than radiation in modifying the acoustic cutoff [@HegHanDe-11aa].

4.  Whether or not the slow wave escapes into the solar atmosphere in strong field regions, the fast wave certainly does. It is immune to the acoustic cutoff effect, but 