soundsystem and speaker stuff

plans

https://www.speakerdesignworks.com/anthology-ii

30 inch sub

https://www.powersoft.com/en/announcement/new-m-force-and-reference-designs

freq plans

: 2..2,5 kHz -> maximum mid horn b&c 8pe21: 400 Hz -> 2.3 kHz low horn b&c 12pe32: 125..150 -> 500 Hz

cubo kick 15: 80 -> 200 Hz hoqs c2e 21: 28 -> 90 Hz

speaker	model	low freq	high freq	delta
ht horn	b&c de500	2 - 2.5 kHz	18 kHz	16000 Hz
mid horn	b&c 8pe21	500 Hz	2.3 kHz	1800 Hz
low horn	b&c 12lw64 replaces 12pe32	140	600 Hz	475 Hz
cubo kick 15	18sound 15nd930 4Ohm	80 Hz	180 Hz	100 Hz
alternativ:
hoqs C-2D-115 Mullins Mod		80 Hz	200 Hz	120 Hz
hoqs c2e 21	18sound 21id oder Precision Devices	28 Hz	90 Hz	62 Hz

tools

https://acousto.sourceforge.net/index.html

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1. Exponential horn basics (the core equation)

A straight exponential horn follows:

[ S(x) = S_t , e^{m x} ]

Where:

• (S(x)) = cross-sectional area at distance (x)
• (S_t) = throat area
• (m) = flare constant (1/m)
• (x) = distance from throat

The flare constant is tied directly to the low cutoff frequency:

[ m = \frac{2\pi f_c}{c} ]

• (f_c) = horn cutoff frequency (Hz)
• (c) = speed of sound ≈ 343 m/s

This cutoff is acoustic, not electrical—output drops fast below it.

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2. Choosing the throat area (very important)

For a cone speaker, the throat area is usually related to the cone’s effective radiating area (S_d).

Rule of thumb:

• Compression ratio = ( \frac{S_d}{S_t} )
• Safe range for cone drivers: 1:1 to 3:1
• Conservative (recommended): ~1.5:1

So:

[ S_t \approx \frac{S_d}{1.5 \text{ to } 2} ]

⚠️ Going smaller:

• Raises distortion
• Kills cone excursion
• Makes the driver sad

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3. Choosing the mouth area (this controls bass)

The mouth must be large enough so the wave doesn’t “see” a sudden impedance change.

For an exponential horn, a solid guideline is:

[ S_m \ge \frac{c^2}{(2\pi f_c)^2} ]

A more intuitive version:

• Mouth circumference ≈ 1 wavelength at cutoff or
• Mouth diameter ≈ λ / π

Example at 100 Hz:

• λ ≈ 3.43 m
• Mouth diameter ≈ 1.1 m
• Area ≈ 1 m²

Yes, horns get big fast. Nature is cruel.

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4. Horn length (this answers most of your wavelength questions)

Horn length is determined by:

[ L = \frac{1}{m} \ln\left(\frac{S_m}{S_t}\right) ]

This is the real horn length equation—not quarter-wave folklore.

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5. About quarter-wave vs half-wave

Quarter wavelength:

• Often used as a minimum practical length
• Gives some loading, but mouth reflection is still strong
• Common in compact or folded horns

Half wavelength:

• Not too long
• Actually closer to ideal loading
• Much smoother impedance transition
• Bigger, heavier, better bass

For exponential horns:

• ¼λ ≈ compromise
• ½λ ≈ excellent

• ½λ = diminishing returns (unless you’re chasing dragons)

Example:

• 100 Hz → λ ≈ 3.43 m
• ¼λ ≈ 0.86 m → short horn
• ½λ ≈ 1.7 m → proper bass horn

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6. Practical design flow (this saves headaches)

1. Pick desired cutoff frequency (f_c)
2. Compute flare constant: [ m = \frac{2\pi f_c}{c} ]
3. Choose throat area from cone Sd
4. Choose mouth area based on cutoff
5. Calculate length using the log equation
6. If it’s too big → raise cutoff or fold it

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7. Quick reality check (cone speakers vs compression drivers)

Cone-driven exponential horns:

• Work best above ~80–100 Hz

• Get massive below that

• Often better paired with:

  • Back-loaded horns
  • Hybrid bass reflex + horn
  • Tapped horns (if you’re feeling spicy)

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TL;DR

• Throat: (S_d / 1.5) is a great start
• Mouth: roughly one wavelength circumference at cutoff
• Length: calculated from flare constant, not just λ/4
• ¼λ: workable
• ½λ: excellent
• Half wavelength is NOT too long—it’s just big