Strings Guitars

It is these factors of the guitar that allow it to produce the specific sounds required to create music. In order to understand music and how guitars produce it, it is helpful to understand the physics of sound. 

Sound is created when the vibration of material bodies causes energy to propagate in pressure waves through a medium, usually air. All forms of musical instruments create vibrations in order to produce the sound waves that make music. 

Guitars are a type of musical instrument called string instruments, meaning that they create their sound through the vibrations of a string. Vibrating strings on a guitar are fixed at both ends and are elastic. When a guitar string is either strummed or plucked, vibrations in the form of waves travel in both directions along the string and are reflected back at each fixed end. 

These waves do not cancel each other out as they reflect back upon themselves, but instead form a standing wave where crests and troughs remain at fixed positions while the displacement of the envelope of the wave as a whole increases and decreases.

The guitar strings act in such a way that they can satisfy the relationship between wavelength and frequency, represented by the equation v = fλ . This equation can be rearranged to f = v/λ, meaning that the frequency of a wave (f) is dependent on both the velocity of the wave (v), and the length of the wave (λ). 

As well, the velocity of the wave traveling on the guitar string depends on the tension of the string (T) and the linear mass density of the string (µ), in fact, “the root frequency for a string is proportional to the square root of the tension, inversely proportional to its length, and inversely proportional to the square root of its linear mass density” . This means that waves will travel faster when the tension of the string is higher and in turn means that the frequency will be higher as the tension is increased (f = v/λ, the v is increasing).

This also means that waves will travel slower on a more massive string, since if the mass is increased, the v will decrease. This relationship between the speed, tension, and mass density can be arranged into a new equation, v = sqrt(T/µ).

When a standing wave vibrates its physical components, the incident and reflected waves, interfere with each other. When this interaction occurs the medium appears to vibrate in segments separated by nodal points and it is not visually apparent that the whole wave is traveling. Since a guitar string has two fixed ends it will behave as a standing wave when either plucked or strummed. The longest wavelength that a string can produce is twice the length of the string.

Mass density is the only other factor that can be significantly and easily changed, a fact easily verified by noting the different thicknesses of guitar strings. Nevertheless guitars are constructed so that the tension of the strings, as well as their mass, are increased together. As a result, strings are made so that the higher the required frequency, the less mass the string will have, as higher frequencies require a higher tension. 

The less mass they have the less tension is needed to achieve the same frequency. It follows that the lower the required frequency, the higher the mass of the string, since a lower tension produces lower frequencies. The greater the mass of a string, the more tension is required. In standard tuning the strings on the guitar are a perfect fourth apart in pitch (except between G and B), therefore the change in mass required such that the tension remains constant can be calculated.

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