Power distribution Equation?

[Pbassred]

I was trying to find a mathematical way of determining the amount of power that different frequencies use, or..... where a crossover aught to be purly from a power distribution point of view. Since audio response is logarithmic, I thought about finding the halfway point useing:

1/2 Log(20000) [for a 20-20KHz signal].

However the answer is only 141Hz. Even if you add in the 20Hz at the bottom, 161Hz doesn't seem right. Any educated thoughts?

[kelticwizard]

I think the way you find the logarithmic halfway point between two frequencies is:

sq rt (20 * 20,000) = 632.456

[soongsc]

The Linkwitz site has a simple spreadsheet to calculate SPL sensitivity for various driver sizes. For one single driver, due to differences in beaming characteristics, a formula works for the specific driver itself.

[jimbo1968]

Originally posted by Pbassred
I was trying to find a mathematical way of determining the amount of power that different frequencies use, or..... where a crossover aught to be purly from a power distribution point of view.

I've yet to find a proper answer to this.

I decided instead to pay attention to the idea of avoiding crossing in the range 300 to 3000Hz.

My system will be 40-200, 200-20k. I'd quite like to know whether one of those bands deserves a bigger amplifier than the other. 50W is more than enough for the 200-20k driver but I could up the power to the woofer if it was required to match the higher range.

[Stocker]

If you listen at very high levels (have to shout to be heard) then you may benefit from higher power amplifiers for low frequencies, especially if you have inefficient speakers.

OTOH, some of the world's most highly-regarded (tube) amplifiers have fewer than 10 Watts and most folks probably use less than a single watt more than they realize.

[soongsc]

Originally posted by Pbassred
I was trying to find a mathematical way of determining the amount of power that different frequencies use, or..... where a crossover aught to be purly from a power distribution point of view. Since audio response is logarithmic, I thought about finding the halfway point useing:

1/2 Log(20000) [for a 20-20KHz signal].

However the answer is only 141Hz. Even if you add in the 20Hz at the bottom, 161Hz doesn't seem right. Any educated thoughts?

I think I understand what you are looking for now.
The equation is N=log (f2/f1) /log 2 where f2 is the upper frequency and f1 is the lower frequency. Get N to be equal between the frequency ranges than you use the same amount of power.

[richie00boy]

Originally posted by Pbassred
I was trying to find a mathematical way of determining the amount of power that different frequencies use, or..... where a crossover aught to be purly from a power distribution point of view. Since audio response is logarithmic, I thought about finding the halfway point useing:

1/2 Log(20000) [for a 20-20KHz signal].

However the answer is only 141Hz. Even if you add in the 20Hz at the bottom, 161Hz doesn't seem right. Any educated thoughts?

Look on the ESP website, Rod has an article covering the very subject. It works out about 330Hz I think for bass-mid.

[Pbassred]

Thanks for the varied replies:
Rich - yes there is an article about bi-amping. which has a table showing 350Hz. Rod tantalisingly says he worked it out but doesn't show the formula. The rest of the table was worked out by Fane so I'm going to take 350 as the righ answer, but I don't know how they got there.

soongsc - Your formula is incorrect unless the answer is 9.8Hz.

Wiz - close, but I don't follow the logic. The root(?) off1 times(?)f2

[noah katz]

Whatever freq you find assumes that energy is equally distributed per freq, and that all the drivers are the same efficiency.

The latter at least is not likely true unless you have a very large box for the bass driver(s), and or accept a highish low freq cutoff.

[jimbo1968]

I've seen that table before, it's one of the examples of incomplete explanation that I was thinking of.

Does it state the assumption it makes about lowest frequency?

Also what if we want 3 bands?