slackerbob said:

1. What influence does the choice of the curve defining the expansion of the horn have over the response?

2. How does the throat area influence the response?

3. Ideally, the horn should be 1/4 long as the lowest wavelength you're covering, correct?

Quick 'n dirty answers:

1. Different expansion curves have different lengths to get to the same mouth size, since 1/4 WL of the lowest freq you want to produce is a minimum, the expansion curves define the lowest freq your horn can safely reproduce for a given mouth size. (it's not that easy, mouth size itself is also a factor, but this is just to give you an idea.)

Also, the longer your horn, the greater your efficienty. A tractrix curve gives less eff than an exponential, and a hyperbolic curve gives even greater eff. Tractrix flares the most, hence is the shortest, hyperbolic was the lowest flare rate, hence the longest.

However, i read from several sources that a hyperbolic gives more distortion in the very low freq, due to air nonlinearities ... pick your posion.

2. Lowpass filter. Smaller throat is less high freq, and more efficiency in the lowest freq. Try to overdo it, and instead of a relative flat responce, you'll get a bass-bump at the lowest freq your horn is designed for, and a rapid fallof above that.

Beware, the M. Leach paper's calcs give a way too small throat area, the only downside of this exellent paper!

3. Yes. A horn is like a pipe sealed at one end, and the first resonance point is at 1/4 WL. I recently looked this up again in my Physics course from my uni days. Guess my memory isn't what it used to be.

Tip: use Hornresp and play with the different parameters, you'll quickly come to the same conclusions.