A guitar produces sound when one of its strings is plucked or strummed. The guitar strings are attached at two points, the head-stock and the bridge. The strings in a typical acoustic guitar are all the same length. However, different sounds can be produced through pressing of the wire against the frets on the guitar. This creates an artificially shorter length, which is also known as the speaking length, of the wire. The speaking length has an inverse relationship with the frequency of the note produced.
The speaking length is the part of the wire which resonates at a particular frequency, resulting in a note being played. When the wire strummed, a standing wave is generated, which can be modeled through the use of:
where v is the velocity of the wave propagation along the wire, T is the tension of the wire, and μ is the mass per unit length of the wire in kg/m. In a guitar, the mass per unit length is changed by the thickness of the wire. In a guitar, the low E string is usually the thickest, followed by the A, D, G, B, and high E strings. The combination of different thicknesses and tensions results in the production of different notes.
Composition of the string is an important consideration, as the elasticity impacts the ease of tuning. Strings that are incredibly elastic are difficult to tune as they require much tightening, while inelastic strings are very sensitive to minor amounts of tightening which greatly vary the tension.
|Young’s Modulus (Pascals) x 109
Figure 1. Values for Young’s modulus for different metals
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