In reply to:
A more powerful amp will play more loudly without clipping, compressing the signal, or otherwise changing the sound
In my opinion, John is "DOBA" accurate in the post above, except that I would add that a more powerful amp will only enable the total volume to be a bit higher....not nearly as much as one would expect.
And now, we segue into JohnK to give us the exact formulas that descibe how much louder more powerfuil amps will be and how many watts you need to have to have a "doubling of perceived volume".
John?
