Merlin's incredibly helpful book goes into this in just enough detail, but the paraphrased version is the 1:10 rule of thumb as disco says.
Their nominal value must be at least 10 times more than the highest source impedance they are likely to be fed signal from.
Normal series pots show 1/4 their nominal value as max output impedance. Occurs at the point of half signal output division.
Their maximum output impedance must be at least 10 times less than the input impedance of the stage they pass signal to.
The 1:10 ratio ensures minimal signal losses both ways. The systems are now properly bridged.
Keeping it low value for average modern sources low impedance is in most cases safe and will not bring problems.
Some input stages have enough capacitance that leads to significant bandwidth limitation when a pot is chosen for higher value than necessary. Because an RC filter is formed by the pot's series output impedance and the input stage's capacitance to ground.
Higher value than necessary is prone to more sensitivity in noise pickup also.
When key parameters are unknown it takes bench experiments to determine. Using function generator, oscilloscope, and rheostat mode series trimmers to measure effects on signal amplitude and frequency in combination with finding and adding proper source impedance, emulating the likely pots max series output impedance, using the actual amp's input. Or by exchanging and turning actual available pots instead of emulating their different output impedance effects under consideration.
It depends if you're talking about designing a circuit from scratch where you have control of the source and/or load, or whether you mean adding a passive volume pot to your existing signal path, where you don't want to start hacking the down-stream equipment. I'll assume the former.
You always want volume pot resistance to be as small as possible to minimise noise and maximise bandwidth, but no smaller. So you need to work out your limits. The upper limit depends on what will be loading the pot, and also how much Johnson noise you're willing to tolerate (often you have little choice over the noise, so just make the pot as small as possible). The lower limit depends on what is going to drive the pot.
When you're designing a whole circuit from scratch you can chose what comes right after the volume pot. Often it will be a valve grid and nothing else. That means you have no load resistance to worry about (it's basically infinite), only Miller capacitance. The source resistance of the pot will form a simple RC filter with the Miller capacitance. Hence if you have, say, 150pF Miller capacitance then you need the source resistance to stay below 50k ohms or the bandwidth will drop below 20kHz. Now, the maximum source resistance of a pot is one-quarter of the total pot resistance; this happens when the wiper is at the -6dB position. Thus we need a pot smaller than 4*50k = 200k ohms. That's your upper limit.
Having figured that out you can then work backwards and ask, what can the driving stage actually cope with? Output impedance isn't the whole story; idle current (headroom or driving capability) is. Maybe you're lucky and the previous stage is an opamp that can happily drive a 10k pot -awesome! Or maybe it's a wimpy 12AX7 cathode follower, in which case we might risk a 100k volume pot, or swallow our pride and stay with 200k. Or maybe it's a better cathode follower that can safely drive a 50k pot? Or maybe it's a gain stage that really needs to see a 470k pot or larger -uh oh, back to the drawing board! Such is analogue circuit design.
But if you want the quick answer; in a valve system you normally want a 100k, 200k, 470k, or 1Meg pot. That's a small range to cope with, so cut and try.
Look in the manual. Or make an educated guess based on the way it's built; if it's all-tube then it's probably between 100k and 1Meg. If it's solid-state then it's probably between 10k and 100k. But you can't know for certain unless you open the hood and trace it.
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