First, let me congratulate you for choosing a maximum 100' distance. While others argue about the longest that string can be, the reality is that every time you connect something to the string to hold it up you dampen the signal. so, ideally you want the pole holding the string up to actually be holding the repeater mechanism such that the string can hang free for highest quality transmission.
Cheap and it looks like it works: perfect government solution
My first solution is to use two funnel-shaped objects. The string is tied to the pointy ends and the whole contraption is mounted on a pole. One half (call it the incoming half) is acting like a megaphone to amplify the signal. The second half is acting as a compressor (think "stethoscope") to apply the signal to the next length of line.
Because no active amplification is occurring, this would only benefit you for a couple of hops. It would need to be soundproofed to ensure the environment (dogs barking, rain falling) didn't drown out the signal.
To amplify a voice effectively, a megaphone should be at least as long as the wavelength of the sound it's amplifying. Because human voices have wavelengths up to several feet long, the best megaphones (like the ones the cheerleaders use!) are usually manufactured as cones that are several feet long. (Source)
Factually, this probably wouldn't work (or, its efficiency would be very low) because you have the same energy going out as you have going in. Megaphones aren't magic. They don't amplify anything. What they're doing is more efficiently transmitting sound waves (e.g., more of the sound you're naturally making is being directed toward where you want it to go).
However, this works both ways and is therefore cool. This won't be the case with our next item.
But we want an actual amplifier, thanks!
Let's use water in the same way you use your car's brakes. the incoming sound is hitting a "master cylinder" full of water. The sound moves through the water to a secondary (and much, much smaller) cylinder. The output of that smaller cylinder will be amplified.
Note that we're not actually trying to move the sound "through" the water (in fact, moving the sound into a third medium simply reduces efficiency). What we're trying to do is move the water. Small movements in the master cylinder translate to large movements in the secondary cylinder.
Factually, sound on a string probably wouldn't create enough audio-force against the surface of the water to get sound out the other end. Water might be too dense to do this with. However, it would make a cool experiment. The concept is sound, just the string might be a problem. The energy coming out the other end is very low. It might actually be easier (or beneficial) to use this other than a simple can to capture the original signal and boost it into the string.
Also, this only works in one direction. You would need two strings, one to hear and a second to speak, for each user.
More complicated solutions
One ore complicated solution is the compressed air gramophone using a pneumatic amplifier.
A pneumatic amplifier was realized by using a sensitive valve, which required little force to operate, to modulate the flow of a stream of compressed air. The basic principle of the valves used in these devices was to pass the stream of compressed air through two partially overlapping combs. The sound vibrations to be amplified were applied to one of the combs, causing it to move laterally in relation to the other comb, varying the degree of overlap and so altering the flow of compressed air in sympathy with the sound vibrations.
This would be the mechanically most complex and expensive solution (also requiring two-way communication), but it would allow you to transmit almost any distance. However, putting one of these every 100 feet would be... impractical. The cost of maintenance would infinitely exceed the value of the solution.