Enormous megaphone from silent film era - photo

[mwmkravchenko]

Is there a specified ratio of length to diameter? Would a longer but narrower horn project sound further?

There are balances. A horns length dictates how low it can support the sound. The size of the mouth ( large end) really dictates how ripple free the sound will be. Ripple as in not exactly like the sound input but rather a bit distorted.

If you are interested there is a great program for designing horns that is free:

Hornresp

And a huge thread on how it works : Hornresp - diyAudio

There is a pretty comprehensive manual built into the program.

Sound projection is more a situation of the correct length to mouth diameter for the frequency range that you are interested in. Human voice is a fairly narrow bandwidth and not that hard to do right.