zumbo said:
Now we are getting somewhere. I look at it like this.
You hook the 8ohm speaker to the 200w amp, 100w at half volume (theoratically).
Now hook the 4ohm speaker to the 200w amp that becomes 350w, so 175w at half volume (theoratically).
Now factor in the sensitivity rating of 89dB for each speaker, and it becomes appearant to me the 4ohm speaker is (theoratically) 75% louder, once again given the amp is 4ohm stable.
Let's say you turn the 200W amp volume up until it develops 100W across that 8 ohm load (you referred to that as "half volume", leave the volume (i.e. the output voltage) exactly where it is and now you replace the 8 ohm load with a 4 ohm load, the current is going to double. Since P=I²R, the power into the 4 ohm load will double, or 200W, not 175W, if the voltage drop at that point is negligible. The question is, whether the voltage drop is linear from 0 to 100% output. If it is, then you are exactly right.
When Mac said, 87dB 4 ohm=84dB 8ohm, I assume he meant in terms of how difficult it is for the amp to drive the load. It is twice as hard for an amp to drive a 4 ohm load because it has to deliver twice as much current at the same volume (voltage). So if the 4 ohm load is 87 dB, that is twice as sensitive as the 84 dB one, it will make it just as easy as the same amp trying to drive that 84 dB 8 ohm speaker as it is to drive the 87 dB 4 ohm speaker. It has nothing to do with which one sounds louder, just which one is easier to drive. I could be wrong, hopefully he will check in eventually and speak for himself.
Buck: impedance is not "simply resistance". Impedance of a component or circuit is the combined effect of resistance, capacitive reactance, and inductive reactance of that component or circuit. The vector sum of all three is know as impedance.
When capacitive and inductive reactance are zero, impedance equals resistance. In the strictest sense it will be difficult to find anything that is purely resistive, inductive, or capacitive but for most practical purposes, resistors are consider to be purely resistive and capacitors are considered to be purely capacitive etc.