4ohm, 8ohm speakers and output power

Assuming that two speakers both have the same sensitivity rating, but one having 4ohm and the other having 8ohm.
For example 88db/watt/meter.

Now usually and in most cases, a given amp can have its output power doubled when driving a 4ohm loud vs. an 8ohm load.

Does this mean that in theory, the 4ohm speaker can play louder than an 8ohm speaker given they use the same amp since the amp can deliver twice as much power to the 4ohm speaker? And since they have the same sensitivity, more power equals more louder.
Nope. First of all, there is no such thing as an 8ohm or 4 ohm speaker. What you have is a speaker with a nominal impedence of 4 or 8 ohms. The actual impedences varies considerably throughout its range. Some nominal 8ohm speakers have droops in the impedence curve to 2 ohms or less, usually in the bass, and rises to 16ohms or more in the mids/highs. Ditto speakers with a nominal rating of 4 ohms. Such speakers present major difficulities for many amps. Impedences droops require more power. An amp that doesn't double its available power to a 4ohm load will clip much earlier when called upon to support the droop in impedence than will an amp which doubles its power into 4 ohms. Hope this description makes sense to you.
Yeah, what Newbee sez : )

A speaker that presents a nominal 4 ohm load will draw twice as much power as a speaker with a nominal 8 ohm impedance. Since the amplifier has to work harder i.e. generates more heat to deliver twice the power, you aren't gaining anything in terms of system efficiency when you go to a lower impedance load with the same sensitivity.

Other than that, you really have to look at how they are rating the sensitivity of the speaker. An 8 ohm speaker with 2.83 volts fed into it that is 88 dB's is measurably more efficient than a 4 ohm speaker that is rated at 88 dB's with the same 2.83 volts. The only time that you can compare sensitivity ratings between different speakers is if they specifically state that they are tested with 1 watt of input. Using a "standardized" voltage like 2.83 is NOT "universal" due to variances in impedance. The 1 watt method takes the impedance into consideration and compensates accordingly.

Another factor to think about is damping factor, which is a HIGHLY misunderstood term. That's something different though, so i don't want to get into that here. I'll just say that a lower impedance speaker has more potential to distort the output of the amplifier as the loading conditions vary dynamically. This is why "beefy" amplifiers typically work best into lower impedance speakers i.e. they typically have a lower output impedance than a smaller amp. The greater the difference in output impedance of the amp and the input impedance of the speaker, the more stable the circuit will become. Since tube amps can sometimes have output impedances as high as 2 - 4 ohms and are typically of a very limited current design, you can see why they would work best with a speaker of higher impedance. Otherwise, you run into problems with the speaker "modulating" the output of the amp. Not only will this change tonal balance and frequency response, but it will also alter distortion and transient response characteristics. This is yet another reason why some components are VERY system dependent i.e. they aren't nearly as stable and require a phenomenal amount of attention to avoid aggravating this problem. The ASL amps and some Cary's come to mind here.

All things being equal, one is typically better off with a high efficiency, higher impedance speaker that isn't real reactive. Having said that, i don't know of any speakers that are made like that which i really like. While this is obviously a matter of personal preference, it just goes to show how theory and reality sometimes don't jive. Sean
Sean: Let's say that the sensitivity is rated using 1W as a reference which says that given an 1W input, both speaker can generate both 88db of sound at 1meter distance. And of course as you said, speaker impedance was taken in account which means that the amp has to apply a higher voltage to generate the same amount of power to a 4ohm speker as opposed to a 8ohm.
(Assume also that the 4ohm speaker always has its impedance lower than the 8ohm speaker in all frequency band from 0 - 22khz)

I guess we can agree that there can be no argue about the rating of the speaker and how it was measured. So let's ignore how efficiently the amp can generate power, and assume that somehow we manage to double the power when we drive the 4ohm speakers, then I don't see how the 4ohm speaker cannot be played louder than the 8ohm speaker.

The only factor that we don't know is that sensitivity may not be linear which means that higher Wattage the 4ohm speaker somehow is less sensitive than the 8ohm speakers but that is another set of specs all together.
Sean, FWIW to others who like tubes but are not aware, your point on amp/speaker matching is right on. One of the big priorities I set when I was matching speakers and amps was getting speakers with a minimum impedence of 5 ohms and 8 ohms nominal - a fairly flat curve I think. I also paid attention to the speakers impedence curves and the amps output impedence curves to make sure they complimented each other. Did I do good?
Andyr: All things being equal ( ha ha ha ), when you go from an 8 ohm load to a 4 ohm load with an SS amp, you double the current capacity or "ampacity" of the circuit. The only problem is, since you've cut the impedance in half at the speaker, current demand is doubled at the amp. As such, IF the amp actually "doubles down" as impedance is halved, you've "theoretically" gained since the amp now has more voltage headroom for peaks. Here's where the reality factor comes in.

Since most amps DO NOT double down as impedance is halved, going to a lower impedance speaker can actually reduce the sonic potential of the system. This is due to increased voltage sag that the amp experiences under heavy loads due to the lack of available current. When you pull more current due to having a lower impedance, you generate more heat. The hotter a device gets, the less efficient it becomes. On top of that, if you're pulling more current, the device also becomes limited in how much voltage it can pass. You have to remember that each device in the circuit is rated to pass a specific amount of wattage. Since wattage equals volts x amps in the circuit, pulling more current means that we have to reduce the available voltage. Lack of voltage means reduced dynamic headroom with more potential for compression or clipping.

Besides all of that and to re-state what i mentioned earlier, the lower the impedance, the more likely the speaker is to "modulate" or "distort" the amplifier's output. This is why i said that one is ALWAYS better off with a higher efficiency, higher impedance speaker. Less heat with less current demand equals an easier load on the amp.

So long as the amplifier has enough power potential at the higher impedance that it is loading into, leave well enough alone. That is, unless you have an amplifier that is capable of delivering as much voltage and current that you would ever need into any given load at any given time at any given frequency. This is a VERY tall order and most amps will fall flat on their face trying to do so, especially with wildly reactive speakers.

For those that want to learn, i would HIGHLY recommend reading the "amplifier white papers" that Bob Carver wrote. His writing is very simple to follow along with and may help you better understand how / why some amps seem to run out of steam when being throttled faster than other amps of similar power ratings but with different design topologies. If it is one thing that i will give the Sunfire amps, they never get "gritty" even when throttled beyond belief. This explains why that is so.

Newbee: Yes, you did good. Then again, you already knew that : )

Depending on the output impedance of your amp though, even 5 ohms may be kind of low. I have to assume that you took that into consideration when arriving at suitable figures though. You don't strike me as being careless in your decisions, so i have to assume that you left enough of a "fudge factor" in play to cover all bases. Sean
If both speakers have the same sensitivity but different nominal impedances (8 and 4-ohms), the one with the 4-ohm impedance will not play louder. The 4-ohm impedance will attempt to draw more current (power) than the 8-ohm, but any extra current (power) it coaxes from the amplifier will be dissipated as heat - not as additional cone displacement. In other words, the speaker acoustic efficiency drops as the nomimal impedance drops. The amplifier notwithstanding.
I was thinking that if the speakers are rated using Volt instead of Watt then the imdedance will be taken into account.

For example if both are rated as 88db/2.89V/meter then they would play to the same loudness. The 4ohm speaker will just draws more current and therefore double the input wattage.

BUT I STILL think if they are using wattage as a reference then the 4ohm must be able to play louder given the same input wattage. I still don't see it any other way.
At the same input voltage a 4-ohm driver will draw 3db more power than an 8-ohm driver. If both drivers have the same SPL at a given watt then, yes, the 4-ohm is louder. Both have the same efficiency.

But now you have two different sensitivities because with the 4-ohm driver you get 1 Watt from 2 Volts whereas you get 1 Watt from 2.83 Volts from the 8-ohm driver.