In sound recording, soundwaves may be manipulated and/or stored in 4 forms ...
Sound in the air takes the form of changing air pressure energy. In order to amplify or record sound we must first convert it into electrical pressure (measured as voltage). This is achieved by means of a transducer, in the form of a microphone. (A transducer is a device for converting one form of energy into another.)
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As a soundwave in the air takes the form of rising and falling air pressure energy, so a soundwave in an electrical cable or circuit takes the form of rising and falling electrical pressure energy (voltage).
A soundwave entering a mic causes a diaphragm to vibrate. Put simply, as the diaphragm moves backwards (when compression hits it) and forward (when rarefaction hits it) it causes a magnet to move inside a coil of wire. In accordance with Faraday's principles of electromagnetism, this induces (creates) an electrical signal in the coil which rises and falls in pressure (voltage) according to the movement of the magnet. Thus a pattern of changing electrical pressure is created which tracks exactly the pattern of changing air pressure energy entering the mic.
In order to capture the detail of the air pressure soundwave, the diaphragm moves microscopically. Thus the electrical pressure soundwave the microphone produces is very low in amplitude. This signal must be sent to a mic pre-amp (perhaps in a mixing desk), via a balanced lead (which protects it on its journey), where it will be boosted to so called "line level".
This signal may then be sent on to either a recording device (tape, A to D converter, etc), or a power amplifier where it is boosted further before being sent to a speaker(s).
In its electrical form, it is extremely difficult to record, or store, sound. A tape recorder is a device which can convert an electrical pressure soundwave into magnetic pressure stored in the oxide of a piece of moving magnetic tape. In this case the conversion is handled by a transducer called a tape head. Magnetic pressure is measured in flux.
In this case, the analogy of "pressure" breaks down. Analogue to digital conversion (essentially the process of converting an electrical pressure soundwave into binary digits) allows a mathematical "description" of a soundwave to be created as a series of numbers (think of a join-the-dots picture) and stored onto a variety of different devices (optical CD, hard drive, RAM, ROM etc).