'Audio', you have my sympathy
...
All of the 'standard' lengths of antennas, 1/4 wave, 1/2 wave, 5/8 wave, etc, are never an exact 50 ohm match without some kind of 'finagling', adjusting of things. The typical input impedance of a 1/4 wave antenna is something around 20-30 ohms, which means that an SWR of around 1.5:1 is the best you can expect. The exceptions are always a 'fluke' of some kind. A 1/2 wave that's center fed is something on the order of 75 ohms. End fed it's well over 1000 ohms typically.
Resonance, which is directly affected by an antenna's length, has nothing to do with input impedance. Resonance deals with there not being any reactance present in the input impedance, only resistance. Impedance is made up of both resistance and reactance. The problem is that reactance doesn't radiate, only the resistance does. Another problem is that an SWR meter doesn't have the slightest idea that reactances even exist, they can't distinguish between reactance and resistance. That means that an antenna that has a 'good' SWR may have lots of reactance present and therefore isn't resonant, and may radiate terribly (reactance doesn't radiate). The opposite is also true, an antenna with a 'bad' SWR might be a very good signal radiator (typically means that there is only resistance present, no reactances, resistance DOES ratiate but may not be the 50 ohms the radio is 'looking' for so high SWR). A matching device basically nullifies the reactances, and transforms the resulting resistance to something close to 50 ohms. That 'matching device' can be a lot of different thingys, a 'ring', 'trombone' looking thing, a tuner, lots of different ways of doing it.
Any antenna radiates all the power that gets to it. The problem is that depending on what the radio 'sees', the radio may not be putting out full power because of a mis-match. Or, if the resulting impedance is highly reactive, and reactace doesn't radiate, there may be some power wasted in it and not radiated.
Confusing, ain't it?
Probably the most common thing to do with a 1/4 wave whip is to 'jockey' the length till the SWR meter says things are 'right'. There's some losses because of that, but, since the radio 'likes' what it 'sees', things sort of even out. May not be the "perfect" combination of characteristics, but if it works, why not? The same holds true for any antenna. The only difference is 'where/how' you do that 'jockeying', sort of.
Now, having said all of that (which you didn't wanna hear), stuff that's not easy to get a handle on, there it is...
- 'Doc
('Audio', still got my sympathies
)