Recall that an inductor blocks higher frequencies while allowing low
frequencies through so, in the top picture, the addition of the
RF Coil has effectively blocked the 10.7MHz signal leaving a clean audio
signal - but, it is still a DC voltage and unsuitable for an audio
With the addition of a large Audio Capacitor, the low frequency audio can
pass through but the DC 'component' of the signal is removed.
The bottom picture shows the final output - a fully cleaned up, AC
audio signal suitable for feeding an audio amplifier.