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[Paul Spencer] = work in progress - help/comments anyone? = * If I have a target length and mouth area, what do I do about expansion contours? * What are the forumulas for other types of expansion contours? ==== ACOUSTIC LENGTH ==== 1/4 frequency wavelength determines the low frequency limit of horn loading wavelength in metres = 344 / frequency (Hz) 20 Hz ~ 4.3m axial length required 30 Hz ~ 2.8m 40 Hz ~ 2.2m 50 Hz ~ 1.7m Please note: this is a minimum; it is preferable to make the horn twice this length, as it results in the horn working in a velocity controlled manner Acoustic length = physical length + (mouth diameter x 0.6) The second part of the equation (mouth diameter x 0.6) accounts for the fact that the effective length extends a little longer than the axial length. ==== MOUTH SIZE ==== This relates to whether it radiates into free space, half space (outdoors on the ground), quarter space (on the ground against a wall) or one eigth space (corner). Each subsequent step requires half the mouth size of the previous 1. free space - requires mouth circumference equal to the wavelength of the LF cutoff 2. half space (outdoors) - as for #1 /2 3. quarter space - as for #1 /4 4. eigth space (corner) - as for #1 /8 For free space horns Mouth Area = Pi * [c / (2 * Pi * f )]^2 ==== FOLDINGS ==== <This section gleaned from John Sheerin - https://ldsg.snippets.org/HORNS/design.html) Parallel walls creates resonances which absorb power from the horn's output if it falls inside the horn's operating band, creating a notch in the frequency response. This resonance would occur at the frequency whose half wavelength is equal to the distance between the parallel surfaces ( f = 344 / x / 2 ). Additional resonances would occur at odd multiples of this frequency (1, 3, 5, etc.). This would indicate that to go higher in frequency using a horn with parallel side walls, one would need a narrower horn (consider the popular Lowther-style rear-loaded horns). Folding can also introduce anomalies into the response. ==== EXPANSION CONTOUR ==== - Conical - Exponential / Hyperbolic (longest) - Tractrix (shortest) Exponential contours are considered best for bass horns. === EXPANSION CONTOUR FORMULAS === ==== EXPONENTIAL ==== The hyperbolic / exponential formula (source: John Sheerin - https://ldsg.snippets.org/HORNS/design.html) ==== Area = Throat Area [ cosh ( x*2*Pi*f / c) + M * sinh ( x*2*Pi*f / c) ] ^2 ==== where x = distance from throat f = the cutoff frequency of the horn M = the flare constant - M = 1 is exponential, 0 < M < 1 is hyperbolic c = the speed of sound, approximately 13538 inches per second or 344 m/s (depends on temperature, etc.) == EXAMPLE == - 40 Hz target cutoff - corner loaded design 1. Target acoustic length 1/2 wavelength = 4.3m 1/4 wavelength = 2.15m 2. Mouth area area = 1/8 x Pi x [c / (2 x Pi x f )]^2 f = 40 hence, area = 1/8 x Pi x [c / (2 x Pi x 40 )]^2 area = 0.7 sqm 3. Length correction correction = 0.6 x mouth diameter = 0.6 x 0.77 = 0.46m 4. Physical length Physical length = 4.3 - 0.46 = 3.84m or 1.7m for quarter wavelength version This is correct assuming both 1/2 and 1/4 wave version have the same mouth area. == COMMENTS == This would make a bass horn with a similar mouth size to the Lab12 which does not require a stack of 4. The length would also be similar to the Lab horn, although it is actually a little longer. This is by no means a design one would build, but a preliminary starting point to give an idea of some numbers to simulate. = next [Bass horn projects online] = |