By "efficiency", I will narrowly interpret this to mean how you can have the loudest
response on the far end per unit loudness on the sending end. To be more specific,
and to use the usual term for efficiency, we want the ratio of the acoustic energy
produced at the receiving end to the acoustic energy directed at the can
at the sending end.
Well, first of all I wouldn’t make the phone out of tin cans. The idea is to have a diaphragm that vibrates and pulls on the string connecting the cans. The base of a tin (or more likely, steel) can is very stiff and is rigidly attached to the side of the can. Speaking into the can will cause the base to vibrate, but will also make the whole can move back and forth as a more or less rigid object (the resonant frequency of the can is fairly high, in the audio range). If the sides of the can are vibrating, then acoustic energy will be coupled to your hand (very lossy, squishy, damping material) and lost. You can mitigate this by holding the tin can on another string, but why go to the bother?
A step up is to use a paper cup. The bottom of a paper cup moves much more freely with respect to the rest of the cup and may lose much less energy when it vibrates. Loudspeaker cones are usually made of paper, and have special mounts on their rims to reduce the mechanical coupling to their supports.
The string is less important -- ideally it should be lightweight and not stretchy. Sewing thread should be good. Heavy rope is a bad idea -- lots of internal rubbing happens when it’s pulled on. The longer the string is, the more lossy it will be (again, internal friction, and also some coupling to the air), so put the cans/cups close together. Usually it’s a good idea to have as much tension in the string as the cups will stand.
If you just want loudness at a very small, localized spot, you can put an ear horn on one end, which you can hold up to your ear to focus whatever acoustic energy you get out into your ear with as little loss as possible.
(published on 10/22/2007)