Luuuuke! I am your crossover math. Ussssse the formulas!
Midrange-Tweeter Crossover Point
15 µF = 1,326 Hz ≈ 1,300 Hz
8.2 µ = 2,426 Hz ≈ 2,500 Hz
Woofer-Midrange Crossover Point
50 µF = 398 Hz ≈ 400 Hz
47 µF = 423 Hz ≈ 425 Hz
This difference may be slightly audible because the inductor is crossing 400 Hz and a gap in frequency response therefore occurs. Non-musician and (non Bud-Fried) humans tend to poorly hear that low, but it may be slightly audible.
Any arbitrary capacitor value may be obtained by adding
in parallel additional capacitors of smaller value. This technique also improves the performance; look up "bypass capacitors" on AK. (Digital circuits use the same technique.)
This crossover point, like all other aspects of speaker design, is a tradeoff, because the B-800 suffers from increasing cone breakup with increasing frequency, but the tweeter, too, has distortion issues, increasing as frequency drops, plus very poor dispersion aka beaming. At the same time, humans acutely hear in the midrange — as Klipsch noted, we live in the midrange — and taking the crossover hit at 1,300 Hz is problematic. Hence the move to a higher frequency and accepting cone breakup as a compromise to avoid overlap and distortion from filter handoff.
Here's what I previously wrote about cone breakup and the B-800:
Consider the two-way systems with an 8" driver, and look at the crossover points which are traditionally set at ≈ 1,500 Hz, as smaller (tweeter) drivers typically becomes unusably beamy around 1,000 Hz, but sometimes as high as 2,000 Hz, but cone breakup of the larger driver is a bigger factor.
Here are some handwavy arguments with rough numbers, as I have not measured the exact diameters of the cone.
Consider the characteristics of an 8" B-800:
// 8 inch diameter driver has a cone — excluding surround — slightly less than 8 inches, guesstimate at 7 inch
Vs = speed of sound at STP = 344 meters per second
Dmax = Diameter maximum = 8" (cone plus surround) = 20.32 cm = 0.2032 meters (cone plus surround)
Dmin = Diameter minimum = 7" (cone only) = 17.78 = 0.1778 meters (cone only, excludes surround)
fmin = minimum frequency before beaming
fmax = maximum frequency before beaming
fmin = Vs / Dmax
= 344 m/s / 0.2032 m
= 1,693 Hz
fmax = Vs / Dmin
= 344 m/s / 0.1778 m
= 1,934 Hz
So best case is ≈ 1,900 Hz, worst case ≈ 1,700 Hz. Hence 1,500 Hz to 2,000 Hz as safe values. Either way, 2,500 is likely too high.
Compare with the 6" B-209, again guessing for 5" as actual cone diameter:
// 6 inch diameter driver has a cone — excluding surround — slightly less than 6 inches, guesstimate at 5 inch
Vs = speed of sound at STP = 344 meters per second
Dmax = Diameter maximum = 6" (cone plus surround) = 15.24 cm = 0.1524 meters (cone plus surround)
Dmin = Diameter minimum = 5" (cone only) = 12.7 = 0.127 meters (cone only, excludes surround)
fmin = minimum frequency before beaming
fmax= maximum frequency before beaming
fmin = Vs / Dmax
= 344 m/s / 0.1524 m
= 2,257 Hz
fmax = Vs / Dmin
= 344 m/s / 0.127 m
= 2,708 Hz
So best case is ≈ 2,260 Hz, worst case ≈ 2,700 Hz. Hence 2,500 Hz as a safe value.
Any of the lower points are problematic, being smack dab in the region where humans acutely hear.