I returned the other unit because it has a tendency to cycle on and off too
much. This one seems have the same tendency, but this one *may* be varying
the off part of the cycle a bit more than the other one. Frankly, I'm not
sure if there is much difference between the two units, other than this one
whistling for a few seconds if the compressor turns on when the unit hasn't
been off for very long.

Both units are the Freidrich 40 pint, made by "L.G. Electronics" with
electronic controls. If the room humidity, as measured by a digital
hygrometer is only in the 40s or 50s, and I set the humidistat all the way
up to the max setting of 70%, the unit will still cycle on and off
frequently. There seems to be some "rule" built into the unit that it needs
to measure the humidity by turning itself on for two minutes...then it will
shut off for anywhere from 2.5 to 6 minutes. The problem is that these
units engage the compressor during the "on for two minutes" to measure the
humidity. It seems to me that if this unit were well designed, it should
not have to engage the compressor AT ALL if set to 70% and the room humidity
is only in the 40s or 50s.

Granted I don't plan on setting it at 70%. The problem is that when
maintaining a moderate humidity, such as 50%, the unit tends to cycle on and
off frequently (such as 2 minutes on, and maybe as low as 2 minutes off)
which seems too frequent. How these units got Energy Star rating is beyond
me? Now that I know that these units were designed to behave this way, I
may choose to keep the current unit and simply leave it running in
continuous mode and use the 2hour on/off or 4hour on/off timer. That should
keep the average humidity moderate without cycling on and off like crazy.
But I'm just hoping the whistling noise isn't a problem.

Ideally I'd like to keep the humidity just under 50% without the extremely
frequent cycling. Not sure if that is a realistic goal with these "under
$150" units. I suppose I could try the 30 pint "mechanical control" model
that has a dial, but I'm not sure if this unit REALLY has a mechanical
humidistat, or if the dial is just tied into an electronic control???

(I could try another brand, but currently there isn't much else available in
the nearby stores)

J.
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This is because of the high pressure being generated by the compressor
upon startup. The noise is different after it's been on awhile because
now there is some residual pressure. It's probably perfectly normal.
As for the unit you returned - why did you return it?
If it was not functioning properly because it was freezing up or not
dehumidifying then the reason it didn't make the noise is maybe because
it never generated the correct pressure within the sealed system in the
first place.