Farview said:
When you change the impeadance the power doesn't go up or down, the wattage does. You will still have the same voltage swing and thus the same volume at any usable impedance. The number of watts changes because of the goofy formula used to determine wattage. However, you still have the same power.
That is not accurate. The formula for power dissipation in loud speakers is not goofy, but based on the science of electrical currents.
Power is a measure of the rate of delivering sound energy to speakers and is usually measured in Watts. As a general rule, the more watts delivered to a single speaker, the louder the resulting sound. While this varies somewhat by speaker, the principal is well established.
The formula for power delivered to speakers, where V is the voltage and R is the impendence is:
P = V*V/R
So if the amp can put out a voltage swing of 10 volts, then an 8 ohm speaker would receive:
P = 10*10/8 = 12.5 Watts
If we connect a 4 ohm speaker instead, the result is 25 Watts. A 2 ohm speaker would yield 50 Watts.
To think of it a different way, consider the original statement that MesaHead had 2 separate 4 ohm cabinets. If you ran 50 watts though a single speaker you would have some volume level. If you then used a second amp and ran 50 watts through the second speaker as well, you would then have two cabinets each receiving 50 watts, and the resulting sound would be somewhat louder. The result is not twice as loud, as the science of power and loudness is a whole other story, but it would be louder.
So if the same amp can put out the same voltage for either an 8 ohm load or a 4 ohm load, then running two cabinets would double the power and increase the volume. However many amps do not always yield the same output for different impedances.
However as Imaduck said, not many amps can handle 2 ohm loads, and damage to either amp or speakers can result if that is tried.
Ed