The Physics of Electric Guitar Pickups
Electric guitar pickups are devices that are used to create an electric current corresponding to the mechanical vibration of the steel strings on a guitar. Electric guitar pickups are often considered to be similar in operation to microphone, but pickups and microphones are, indeed, different devices. A microphone has a small diaphragm that is vibrated by sound waves, a permanent magnet, and a wire coil that is attached to the diaphragm and moves inside the magnetic field of the magnet. An electric guitar pickup, on the other hand, has the coil wound around the permanent magnet and a steel string that moves within the magnetic field of the permanent magnet.
In both cases, a change in magnetic flux (a measure of the magnetic field strength) through the coil induces a current in the coil. The major difference between the two is that only the vibration of the steel strings is picked up by the electric guitar pickup, not sound. This leads to some distinct advantages in amplification: random sounds and actions cannot be heard through the amplifiers when electric guitar pickups are used rather than microphones.
The pages that are linked to this one more thoroughly explain the theory behind the concept as well as the use of electric guitar pickups
The Theory Behind Electric Guitar Pickups
An electric guitar pickup primarily consists of a coil of wire called a bobbin and a permanent magnet placed underneath each guitar string:
One pole (or a pole piece) extends upward through the bobbin, and the string is positioned immediately over the top of the pole piece. Each bobbin and pole piece is underneath each string, and usually, all of the pickups share one magnet and merely have different pole pieces.
The guitar string is primarily steel, with the heavier strings usually being nickel wound (on a normal six string electric, the heaviest three are wound and the lightest three are single strands). The movement of the ferromagnetic substance (the guitar string) in the magnetic field of the permanent magnet causes the flux through the bobbin to change. Since the bobbin is a good conductor, the change in magnetic flux is opposed in the bobbin by the induction of an alternating current. The change in magnetic field that is created from the AC current is opposite to that of the change in magnetic field in the bobbin. This is created due to a principle known as Lenz's Law. The reason for the induction of an alternating current in the bobbin rather than a direct current is due to the motion of the of the string: the string moves both towards and away from the pole piece of the pickup in the same way that the voltage of an AC current increases and decreases (switches directions).
The movement of the strings that is most relevant to the production of the signal by the pickups is the movement of the string towards and away from the pole piece (vertically in the illustration above). The strings actually move more typically in a rotating elliptical path, but for simplified purposes, they are considered to move in two different directions: vertically and horizontally. In the vertical movement of the strings, the magnetic flux increases as the strings get closer to the body of the guitar and then decreases while the strings move farther away from the body. A change in magnetic flux is also caused by the horizontal movement of the strings, but this does not produce the same signal: the string, starting from the farthest distance to either side, moves towards the center and then away, and then back towards the center and then away. In this short cycle, the flux switches back and forth twice (increases, decreases, increases, decreases). The musical importance of this is that the signal produced has a frequency twice as high as in the case of the vertical motion of the string. Just from this, it can be noted that the sound produced by a guitar is not just a simple first harmonic wave formation, but a much more complicated interaction. If the patterns of vibration of the strings are included in the discussion, then the produced signal becomes even more complicated.
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