Flare comparison

This sheet draws five flare laws between the same throat and the same mouth, all designed for the same cut-off $f_c$. The cone has no cut-off of its own, so it is given the length of the exponential horn for a fair comparison of loading per unit of depth.

What to look for

• Length. The tractrix and spherical-wave horns open rapidly near the mouth and reach it sooner than the exponential. The hypex with $T$ below one is the longest.
• Loading near cut-off. In Fig. 2 the hypex resistance rises earliest; the cone lags far behind and only approaches $\rho c/S_t$ several octaves up.
• Ripple. All five share one mouth, so differences in ripple come from how abruptly each flare ends. Shrink the mouth with the slider and watch every curve get rougher.

Limits of the comparison

The impedance curves come from one-dimensional (Webster) horn theory, which assumes the wave-front area equals the cross-section. That is accurate for slowly flaring horns and optimistic for the last part of a tractrix or spherical-wave flare, where the real wave-front is strongly curved. Directivity, which often decides the choice in practice, is not shown here at all.