Ideal shunt and series resistances for passive attenuators

Your question sounds ambiguous or open top several interpretation.

Do you mean "source " as in CD player /record deck or do you mean "source " as in --source of music in relation to the human ear - IE- a loudspeaker ?

If a loudspeaker then this simple explanation is relevant to your question ---or not ?

L-PADS

and you then mean ---without the potentiometer as illustrated .
 
"Without the imposed constraint of a potentiometer "-- virtual volume control software is pretty sophisticated now but the other section on that potentiometer link relates to impedance in relation to frequency , I have found a Paper relating to various University professors on the subject of virtual impedance matching.

Reactive power matching etc .
 
It would be between 2k and 10k, so around 5k is reasonable.

Yes, that is where today's sources like CD players DVD players & streaming, requiring passive attenuation sound best.

We can see the potentiometer that most users experience, is incorrect, it suffers from trying to apply a comfortable listening range - balancing this against being able to silence volume.
and failing to be a comfortable device to use
 
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It's actually a fun and surprisingly not-simple math problem: Figure out how to use seven relays and as many resistors as you please, to build a relay-switched passive attenuator whose 27 = 128 possible settings, are

0 dB, -1 dB, -2 dB, -3 dB, -4 dB, ..., -125 dB, -126 dB, -127 dB​

Of course you probably want the front panel LCD display to show positive numbers rather than negative dB's. People expect that "50" should be louder than "10" !!



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