This is indeed what happens only if the VFO and an incoming single are
at almost the same frequency ("zero beat"). However, in practice, if
the signal is a cw signal, we listen to a signal that is 600 Hz or so
away from the VFO so that we hear the 600 Hz tone difference.

For a SSB signal, we listen to the audio content contained in the
sideband, which is 300 Hz to 3 KHz away from the VFO signal when it is
tuned in correctly.

- Dan, N7VE

Joel Kolstad wrote:

I'm curious... with the current popularity of simple (e.g., QRP usage)
direct conversion receivers, whatever happened to the problem of having to
synchronize the cariier phases? I'm looking at Experimental Methods in RF
Design, and they just use an LC oscillator for the input to the mixer. If
input carrier is cos(f*t) and the LC oscillator is generating cos(f*t+phi),
where phi is the phase offset between them, you end up with a cos(phi) term
coming out of the mixer. If the frequencies are ever-so-slightly off, phi
essentially varies slowly and cos(phi) should slowly cause the signal to
fade in and out.

Why isn't this a problem in practice?

Thanks,
---Joel Kolstad