I would not use an audio amplifier, far to complicated, Also note you would need a stereo audio amplifier, to get a nice symmetrical waveform at the output.
The simplest solution is probably some kind of motor driver H-bridge IC, combined with an oscillator (Maybe a NE555). You could build it with a few NE555's and drive the wires with that too, but you would be limited to it's maximum voltage (Which also happens to be 18V (I thought it was only 15V)).
It's important to make it symmetrical to avoid galvanic corrosion as much as you can. Preferably you also put a capacitor in each line so no DC can pass at all.
Uh--??
(To unpack that:
1. A linear audio amplifier is already symmetrical. A "half bridge" or "totem pole" design is typical, so, there's a positive swing and a negative swing. If one were missing,
it wouldn't be linear.2. Switching (class D) amplifiers are quite popular, highly efficient, and readily available these days; with a filter network provided, they are electrically equivalent to (1).
3. If the output were DC biased (offset), it would cook speakers just as quickly as it would corrode the wires here. Even if the amplifier is such a bad (or archaic) design that a coupling capacitor is required to use it... I mean there you go, coupled and done. Such designs haven't been in use since the 1960s, and who knows if this is what the above had in mind?
4. A stereo amp does nothing here. Where is the other channel going?
5. If both channels go to each wire, then, that's not stereo, they'd be driven equal and opposite, there's nothing stereo about it, it's mono by definition. The word commonly used for this is "bridged". The resulting H-bridge topology doubles the voltage output from a given supply voltage, which can be handy.
6. The whole thing is floating, battery and solar, no ground connection required -- only the wires laying on the ground provides any earth reference, by way of leakage to it. It's SELV, it's not mains powered, no isolation required. Even if a strongly-offset amplifier were used, the offset can simply be subtracted out, say with a battery (or again, dropped passively with a coupling capacitor), and any offset between the device and earth is simply determined by the resistor divider (sort of) between wires and earth.
As a rule, I try to avoid (ignore) posts that aren't contributing [much] to a thread; but this one seems so exceptional, in how irrelevant it is to the present thread, and, seemingly, out-and-out mistaken, that I feel it necessary to point out the disconnects, and misinformation.)
Tim