Two sonic disruptors
A sonic disruptor is a weapon that projects a focused beam of extremely high intensity sound at its target. The vibration of acoustic energy imparted by this beam disrupts the molecular, and perhaps even atomic, structure of the target, creating a sonic disruption. Sonic disruptors have appeared in weapons ranging from man portable firearms to immense planetary defense batteries.
Most weapon technology in use on Eminiar VII (and presumably, Vendikar) in the late 23rd century was of this type. Hand weapons could stun and kill individuals, and could do considerable damage to objects. Planetary defenses based on the same principle could project sonic vibrations equal to "18 to the 12th power decibels" at starships in orbit around the planet. Even at that intensity, the weapons were not a threat to a starship with shields rigged; they could do little beyond shaking the ship a bit, and their maximum range was less than that of shipboard phasers of that era. (TOS: "A Taste of Armageddon")
Background
There are several technical glitches here. First and fundamentally, sound does not travel in a vacuum; it requires some kind of medium through which the vibrations can propagate. Presumably, Eminiar's scientists solved this problem.
There is an alternative way of explaining this phenomenon: We have been told several times during the show that the orbit of the Enterprise will decay rapidly if she loses engine power. Since the mass of the Enterprise is colossal, this means that it is ordinary for starships of the 23rd century to follow very low orbits, sometimes getting closer then 50 kilometers to the ground. Atmospheric pressure at such altitudes is low, but not low enough to prevent the propagation of sound.
Second, "18 to the 12th power decibels" by itself is somewhat meaningless, since the decibel is a relative unit. Perhaps the 0dB reference point is something all Starfleet officers know, and only we viewers are baffled. Finally, since the decibel scale is logarithmic, 18 to the 12th power is a staggering amount of energy, since one would have to calculate the base 10 antilogarithm of a sixteen digit number. Perhaps the method of reporting values, or the meaning of the unit, has changed by the time of the 23rd century.