Let's say we have a 3 way speaker (tweeter, midrange, and woofer) with 100 watts RMS. How are these 100 watts allocated to the various drivers? I would figure that most of the watts would go to the woofer, and the least would go to the tweeter. Is there a general rule of thumb on this? Is there something more exact?
We often get asked this question, in one form or another.
The power is set primarily by the program. Other factors include the driver sensitivities, crossover point and order of the crossovers.
So the power distribution will vary instant to instant as the program progresses.
There is a useful rule of thumb though that the acoustic power distribution for most program divides at 400 Hz. So the power in program in my experience is concentrated between 100 Hz and 2.5 kHz. Power rapidly falls off below 80 Hz. There is significant power still between 2.5 KHz and 5 to 8 KHz but falling with frequency. Power demands rapidly fall after 8 KHz. Now all this is predicated on natural instruments with the exception of pipe organs, especially those of the Baroque era and their modern copies. The mid range and HF output of these instruments can be, and often is enormous, especially playing the great monumental organ works of J.S. Bach. Electronic instruments especially Synths which can, if asked, output all their power in the 10 to 20 K range and burn out tweeters.
Now there is the myth that there is huge power below 80 Hz, so a sub unloads a receiver. This is not true. It seems that way because for domestic tranquility people want small subs, which are highly inefficient and require high drive power as a result. A bass system optimally sized actually requires very little power to drive it below 80 Hz and down to 20 Hz.
Now in general, a woofer is less sensitive than a mid range or tweeter and so requires more power for a given acoustic output. This is far from always true. However unless a system has an active electronic crossover, a woofer must never be more sensitive than its associated mid and HF drivers, as there is no passive crossover solution for this circumstance.
The other issue is baffle step compensation which is related to the half space, full space transition of monopole speakers. The narrower the cabinet the higher the frequency where this transition occurs and requires a 6db boost below the transition. Unless the crossover to the woofer is very low, then the bulk of this 6db boost falls to the woofer. So that's a two fold increase in power for the woofer in that power range.
The next issue is crossover order. A first order crossover has a lot of overlap between drivers and therefore power over lap. Power drops off at 6 db per octave per order above and below crossover point.
I would say, the power requirements for the mid range in three ways is very frequently underestimated by designers. This is just one of many reasons that make three ways so difficult to design and get right.
So you asked a question with no definite answer, but of importance to consider in speaker design. It is an issue where there is no substitute for experience.
