Horn profiles

OS waveguide

Geddes’ oblate spheroidal contour that leaves the driver with parallel walls and bends onto the coverage cone.

Sheet: 06 / 25
Units: Metric
Air: 20 °C

Fig. 1Axial section, to scale. Dashed is the asymptote

OS waveguideAsymptote

Mouth diameter $d_m$: 221mm
Pattern control from: 1254Hz
Wall angle at mouth: 44.8°
Of asymptote: 99.6%
Mouth area $S_m$: 385cm²
Throat area $S_t$: 5.07cm²
Air volume: 1.45L

Fig. 2Throat impedance of this finite horn

ResistanceReactancedrag on plot to read

Normalised to ρc/St. A waveguide loads the driver much like a cone of the same angle, so set crossover points by directivity and excursion, not by a flare cut-off.

Table 1Build stations

Stations

#	x (mm)	⌀ round (mm)	□ side (mm)	area (cm²)
0	0	25.40	22.51	5.067
1	9.167	31.34	27.78	7.716
2	18.33	44.61	39.54	15.63
3	27.50	60.58	53.69	28.83
4	36.67	77.61	68.78	47.31
5	45.83	95.12	84.30	71.06
6	55.00	112.9	100.1	100.1
7	64.17	130.8	115.9	134.4
8	73.33	148.8	131.9	174.0
9	82.50	166.9	147.9	218.9
10	91.67	185.1	164.0	269.0
11	100.8	203.3	180.1	324.5
12	110.0	221.5	196.3	385.2

How it works

Earl Geddes’ waveguide contour leaves the driver with parallel walls, so the flat wave-front from the phase plug is accepted without a kink, then bends smoothly onto a cone of the chosen coverage angle. In oblate spheroidal coordinates a surface of constant angle is a hyperboloid of one sheet, whose section gives the wall radius at a distance $x$ from the throat as

r(x) = \sqrt{r_t^{2} + x^{2}\tan^{2}\theta_0}

At the throat the slope is zero, so the wall is parallel to the axis. Far from the throat the radius tends to $x\tan\theta_0$ , a cone of half-angle $\theta_0$ whose apex lies in the throat plane. The second trace in Fig. 1 is that cone.

Wall angle

The local wall angle shows how far the contour has progressed toward its asymptote:

\tan\varphi(x) = \frac{dr}{dx} = \frac{x\tan^{2}\theta_0}{r(x)}

A waveguide that is too shallow never gets close to $\theta_0$ and its real coverage is narrower than intended.

How low the pattern holds

The contour only controls directivity while the mouth is large compared with the wavelength. The sheet uses Keele’s empirical rule with the mouth diameter $d_m$ in metres and the included angle in degrees:

f \approx \frac{25\,000}{2\theta_0 \cdot d_m}

Practical notes

Match the throat diameter and, ideally, the exit angle of the compression driver. Many drivers have a conical exit of a few degrees.
Blend the mouth into the baffle with a generous radius to reduce diffraction; that round-over is not included in the table.
Loading at low frequencies is similar to a cone of the same angle, so crossover points are set by directivity and excursion, not by a flare cut-off.

E. R. Geddes, “Acoustic Waveguide Theory”, J. Audio Eng. Soc. 37 (1989), and “Acoustic Waveguide Theory Revisited”, JAES 41 (1993).

Loading sheet…

x (mm)

⌀ round (mm)

□ side (mm)

area (cm²)

25.40

22.51

5.067

9.167

31.34

27.78

7.716

18.33

44.61

39.54

15.63

27.50

60.58

53.69

28.83

36.67

77.61

68.78

47.31

45.83

95.12

84.30

71.06

55.00

112.9

100.1

64.17

130.8

115.9

134.4

73.33

148.8

131.9

174.0

82.50

166.9

147.9

218.9

91.67

185.1

164.0

269.0

100.8

203.3

180.1

324.5

110.0

221.5

196.3

385.2

How it works

r(x) = \sqrt{r_t^{2} + x^{2}\tan^{2}\theta_0}

Wall angle

The local wall angle shows how far the contour has progressed toward its asymptote:

\tan\varphi(x) = \frac{dr}{dx} = \frac{x\tan^{2}\theta_0}{r(x)}

A waveguide that is too shallow never gets close to $\theta_0$ and its real coverage is narrower than intended.

How low the pattern holds

f \approx \frac{25\,000}{2\theta_0 \cdot d_m}

Practical notes

Match the throat diameter and, ideally, the exit angle of the compression driver. Many drivers have a conical exit of a few degrees.
Blend the mouth into the baffle with a generous radius to reduce diffraction; that round-over is not included in the table.
Loading at low frequencies is similar to a cone of the same angle, so crossover points are set by directivity and excursion, not by a flare cut-off.

E. R. Geddes, “Acoustic Waveguide Theory”, J. Audio Eng. Soc. 37 (1989), and “Acoustic Waveguide Theory Revisited”, JAES 41 (1993).

OS waveguide

Inputs

How it works

Wall angle

How low the pattern holds

Practical notes

Inputs

How it works

Wall angle

How low the pattern holds

Practical notes

§ How it works

Wall angle

How low the pattern holds

Practical notes

§ How it works

Wall angle

How low the pattern holds

Practical notes

How it works

How it works