An amp will put out more wattage with a 4-ohm speaker then an 8-ohm speaker. Does this mean that with everything else being equal will a 4-ohm speaker be louder then an 8-ohm speaker?

No. Impedance has nothing to do with loudness. If a particular 4 ohm speaker is significantly less efficient than a given 8 ohm speaker, it could play less loudly, even if it is supplied with more wattage input.

Efficiency is the rating which determines how loud a speaker will play for a given wattage input. In addition, there is a very definite limit to how loud a particular speaker will play before destruction, and this is determined by characteristics of it's design, usually involving more cost for more robust parts.

Efficiency is rated as a certain number of decibels sound pressure when a speaker is supplied with one watt of power, at a distance of 1 meter. A typical rating might be 89db for 1 watt. A difference of 3dB equals an efficiency difference of a factor of 2. A speaker with a rating of 89db will play twice as loud (3db louder) as a speaker rated at 86db when supplied with 1 watt, regardless of it's impedance.

It's worth noting that the ear does not hear 3db as subjectively "twice as loud" - as a matter of fact, 3db is just audible as a loudness increase (or decrease). To make a subjective difference of being "twice as loud", the increase must be around 10db.

Here's a simple question whose answer I should but do not know.

I bought some KEF tweeters just as backup since they are hard to get. Several ae 8 ohms. So......

If speaker systems with x-overs in cabinet are rated at 4 ohms, and you have a replacement driver at 8 ohms....any problem in using it, for example as a replacement?

TIA

Possibly. The efficiencies may be different between the 4 and 8 ohm parts.

The parts values in the crossover were arrived at with calculations using the 4 ohms impedance. If you use an 8 ohm driver in place of an original 4 ohm driver, the crossover frequency will change for that driver, and any voicing applied to that driver will be changed.

I would certainly not install a driver with a different impedance than the one being replaced.

However, I would check that the driver you're replacing is really 4 ohms. Just because the total system is 4 ohms doesn't mean the drivers are automatically 4 ohms.

If you have an ohm meter, check the DC resistance of the voice coils - an 8 ohm driver will measure about 6 ohms, and a 4 ohm driver will measure about 3 ohms.

I understand efficiency and that a more efficient speaker is going to be louder at a given wattage than a less efficient one. I'm asking about the system of an amp and speaker. Some subwoofers have dual voice coils and if they are both 4 ohms you can wire it as 2 or 8 ohms. Will the system, as a whole, be louder if wired at 2 ohms than at 8 ohms?

Dual coil subwoofers are usually made for car audio, where 2 ohms is sometimes used in order to get more power out of an otherwise conventional amplifier (most car power amplifiers now use voltage inverters to get around this).

The amplifier should deliver more power at lower impedances. I would not under any circumstances attach a 2 ohm load to any home theater amplifier.

Whether the speaker will be louder - why don't you hook it up and see?

Regarding the speaker with dual 4 ohm windings. The speaker will pull more power from the amp with the windings in parallel (2 ohms) than it will with them in series (8 ohms) and will play louder. You must be sure that the amplifier is designed to function at a 2 ohm load. There may be problems with sourcing that much current, thermal overload, or stability.