Sound is vibration. Vibration is a wave. Waves are measured by the number of peeks that travel through a medium per second; this amplitude is known as a hertz. When plucked, any given string on a guitar vibrates at a certain frequency, translating that frequency to the air around it. If the string oscillates up and down 20,000 times per second, the air around said string is pushed out of the way 20,000 times a second creating a wave of 20,000 hertz. But without a hollow body to serve as an amplifier for those waves, then how does an electric guitar create sound at concert level decibels.
An electric guitar creates its sound through the pick-up. A pick-up is a set of small cylindrical magnets set directly below each string. The guitar string itself is made from magnetic metals, so as it vibrates, it tugs and pulls on the magnetic field at the exact same frequency as the vibration. This high speed wavering of the magnetic field of the pick-up (plus a copper coil and other items) creates small electric pulses, again in the exact same frequency as the vibrating string. These small, quick pulses of electricity are then carried down a small wire to the input jack, and then through another cord to the amplifier.
The amplifier is basically a pick-up in reverse. Barring other details, the rapid pulses of electricity are carried to the speaker of the amp, again at the same frequency of the vibrating string. These pulses run through a magnet surrounding a copper coil. The pulsing electricity then causes a diaphragm to expand and contract, and you guessed it, it is at the same rate of vibration emanating from the string. Rapidly vibrating, the diaphragm pushes the cone of the speaker, which pushes the air and creates a wave that travels to your ear. Once in your ear, these waves vibrate a set of small bones and are then are turned back into electrical impulses and carried to your brain.