Horn profiles

Hypex horn

Salmon’s hyperbolic-exponential family. Trade a longer horn for stronger loading near cut-off with the T parameter.

Sheet: 02 / 25
Units: Metric
Air: 20 °C

Fig. 1Hypex section against the exponential

Hypex T = 0.6Exponential (T = 1)

Length $L$: 181cm
vs exponential: +7.2%
Mouth $d_m$: 109cm
Reference length $x_0$: 54.6cm
Resistance at $1.2\,f_c$: 0.995ρc/St
Air volume: 257L

Fig. 2Throat impedance of this finite horn

ResistanceReactanceR, infinite horndrag on plot to read

Normalised to ρc/St. Solid traces: this horn, cut into conical elements and terminated by a baffled-piston mouth. Ripple is the mouth reflecting part of the wave back to the throat.

Table 1Build stations

Stations

#	x (mm)	⌀ round (mm)	□ side (mm)	area (cm²)
0	0	50.00	44.31	19.63
1	150.5	60.29	53.43	28.54
2	301.1	75.18	66.62	44.39
3	451.6	95.81	84.91	72.10
4	602.1	123.8	109.7	120.3
5	752.7	161.2	142.9	204.1
6	903.2	210.9	186.9	349.4
7	1054	276.8	245.3	601.7
8	1204	363.8	322.4	1040
9	1355	478.6	424.2	1799
10	1505	630.0	558.3	3118
11	1656	829.6	735.2	5405
12	1806	1092	968.2	9374

How it works

Salmon's hyperbolic-exponential family, usually shortened to hypex, adds one shape parameter $T$ to the exponential law:

S(x) = S_t\left[\cosh\frac{x}{x_0} + T\,\sinh\frac{x}{x_0}\right]^{2}, \qquad x_0 = \frac{c}{2\pi f_c}

$T = 1$ collapses to the plain exponential horn.
$T = 0$ is the catenoidal horn, which leaves the throat with zero wall slope.
$T \to \infty$ approaches a cone. Classic commercial hypex horns sit around $T \approx 0.5$ to 0.7.

What T buys you

With $\mu = f/f_c$ , the normalised throat impedance of the infinite horn is

z_t = \frac{\sqrt{1-1/\mu^{2}} + j\,T/\mu}{1-(1-T^{2})/\mu^{2}}

Lowering $T$ below one makes the resistance rise faster just above cut-off and even overshoot $\rho c/S_t$ , so the driver is better loaded in the bottom octave. The price is a slower initial expansion: the sound stays at high pressure over a longer path, which raises second-harmonic distortion from air non-linearity at high drive levels, and the horn gets a little longer for the same mouth.

Length

With $q = d_m/d_t$ , the mouth is reached at

L = x_0\,\ln\frac{q+\sqrt{q^{2}-1+T^{2}}}{1+T}

Fig. 1 overlays the exponential horn of the same cut-off, throat and mouth so you can see where the hypex stays narrower.

Loading sheet…

x (mm)

⌀ round (mm)

□ side (mm)

area (cm²)

50.00

44.31

19.63

150.5

60.29

53.43

28.54

301.1

75.18

66.62

44.39

451.6

95.81

84.91

72.10

602.1

123.8

109.7

120.3

752.7

161.2

142.9

204.1

903.2

210.9

186.9

349.4

1054

276.8

245.3

601.7

1204

363.8

322.4

1040

1355

478.6

424.2

1799

1505

630.0

558.3

3118

1656

829.6

735.2

5405

1806

1092

968.2

9374

How it works

Salmon's hyperbolic-exponential family, usually shortened to hypex, adds one shape parameter $T$ to the exponential law:

S(x) = S_t\left[\cosh\frac{x}{x_0} + T\,\sinh\frac{x}{x_0}\right]^{2}, \qquad x_0 = \frac{c}{2\pi f_c}

$T = 1$ collapses to the plain exponential horn.
$T = 0$ is the catenoidal horn, which leaves the throat with zero wall slope.
$T \to \infty$ approaches a cone. Classic commercial hypex horns sit around $T \approx 0.5$ to 0.7.

What T buys you

With $\mu = f/f_c$ , the normalised throat impedance of the infinite horn is

z_t = \frac{\sqrt{1-1/\mu^{2}} + j\,T/\mu}{1-(1-T^{2})/\mu^{2}}

Length

With $q = d_m/d_t$ , the mouth is reached at

L = x_0\,\ln\frac{q+\sqrt{q^{2}-1+T^{2}}}{1+T}

Fig. 1 overlays the exponential horn of the same cut-off, throat and mouth so you can see where the hypex stays narrower.

Hypex horn

Inputs

How it works

What T buys you

Length

Inputs

How it works

What T buys you

Length

§ How it works

What T buys you

Length

§ How it works

What T buys you

Length

How it works

How it works