Physics of an Acoustic Guitar
I have been watching my husband play the guitar in a band for five years and he has made it look so easy to make such beautiful music. Most guitar players have progressed with the technology of electric guitars, but when my husband picks up an acoustic guitar and starts to play a song for just me, I hear his love for me in the sounds that he produces. Imagine my surprise when a physics class conveyed to me that there was much more to his playing than I had imagined.
The sound that a guitar makes is easily recognizable to many people because the physics of the acoustic guitar is mostly universal. The noticeable distinctions are the result of various wavelengths and the harmonics that are created by the sounds of the strings on the guitar. The different sizes, tension, and lengths of the strings control these wavelengths. Even by the various guitar body compositions affect the sounds that we hear.
An acoustic guitar has 6 strings that are attached to the top, called the head, and continue down the neck of the guitar to a plate on the body, called the bridge. One end of the string lays on a raised bar on the head of the guitar, called a nut, and the other end lays on a raised bar on the bridge of the guitar, called a saddle.1 Strumming a string on the guitar, either with a pick or with your fingers, causes it to vibrate. These vibrations are waves and they “travel in both directions along the string and reflect back and forth from the fixed ends.”2 As the waves pass through each other from end to end, they create the different harmonics or overtones that are unique to the sound of the guitar.
A node is present on a wave when the string is in its original position. Therefore, where the string lays on the nut and the saddle, a node is present. The section that is the farthest from the original string position is called an antinode, representing the amplitude of the wave. An antinode is present at the furthest amplitude above the string and at the furthest amplitude below the wave. A full wavelength has two nodes and two antinodes.
On a fixed string, nodes are created at both ends, so the fundamental, or longest, wavelength that could be produced, would be twice the length of the guitar string. Harmonics are determined by “whole number multiples of the fundamental wavelength.”3 They can vary in speed and have any number of wavelengths that can be generated with nodes at both ends. For example, the first harmonic would be a full wavelength and have two nodes and two antinodes. Each additional harmonic would add an additional half of a wavelength to the string.
The relationship between the wavelength and the speed of the wave creates different frequencies from the guitar. The frequency is the number of wavelengths that occur per second. The equation is set up as the frequency equals the speed of the waves divided by the wavelength, or f = u § l . Frequency is measured in Hertz (Hz) and humans can...