darrin_h2000 said:
Uh ... I guess that would be me.
It is? Where, exactly?
and the unit for power is wattage=current x voltage.
Yes ... so?
What matters is that wattage = voltage
squared divided by resistance. This isn't in any way inconsistent with your equation: in fact, you can derive one from the other if you also know that voltage = current divided by resistance.
To put this in terms that I hope are sufficiently simple, the equation you've set out doesn't tell the whole story (in this application), because when you increase voltage in a given circuit, you also increase current by the same proportion. So when you double the voltage, you also double current, and wattage increases by a factor of four (two squared).
and the relationship to dB from wattage is logrithmic.
I suppose this is more-or-less accurate. dB is a logarithmic scale that is used to describe particular power (wattage) levels.
And relitive volume doubles every 6 dB.
This is sufficiently vague and ill-stated that I think it requires some clarification.
A doubling of
voltage is a six decibel change (+6 dB) by definition (as noted in my post above).
A doubling of power (wattage) is a three decibel change (+3 dB). A quadrupling of power is a six decibel change (+6 dB). While this might seem inconsistent with the preceding paragraph, it isn't ... because when you double the voltage into a particular circuit, you quadruple the power.
"Relative volume" is a shakier concept, as it depends entirely on what you think "volume" means. If you mean "loudness, as perceived by a listener," I think anyone who's ever fooled around with a mixer or something with a VU meter has noticed that a 3 dB change (doubling the power to the speaker) doesn't sound a whole lot louder. In fact, it's hardly perceivable. Actually, I think little tests have shown that a typical person subjectively describes a
10 db change (ten times the power!) as about "twice as loud."
In a slightly different, though related context, this is why people sometimes also say, as a rule of thumb, that you need to cut a guitar amp's power by a factor of ten to cut the "loudness" in half: a 5-watt amp sounds
about half as loud as a 50-watt amp.
[A caveat: all of the above is somewhat simplified ... for one thing, I've used DC equations, which are ok for AC for the purpose of the general conceptual framework, but if you really wanted to get this all perfect, you'd need to introduce some complications like capacitance, inductance and some other words I can't remember at the moment].