The Acoustic guitars are subtle and melodious but what

The acoustic guitar is the the most played instrument in the music world. Though, the guitar looks like a simple instrument to play there are a lot of physics regarding sound behind the creation of it, from the strings to the air inside, the anatomy, and the sound spectrum. Acoustic guitars are subtle and melodious but what makes it sound irresistibly good are the physics behind the instrument itself. Physics plays a huge part in acoustic guitars in many ways, including the structure of the guitar, the effect the physical structure has on sound, wavelengths, mathematical insight about guitars, and research that has been done to improve the sound.The modern acoustic guitar is the descendent of stringed instruments dating back from some of the earliest civilizations known to humanity. Predecessors of the acoustic guitar include instruments such as the harp and the lute. While instruments extremely similar to the acoustic guitar were being built in the pre 17th century 1, modern guitar designs didn’t begin to appear at the beginning of the 1880s 2. Figure 1 3 (left) and Figure 2 4 (below-left;) both show the design of modern guitars; however some acoustic guitars are different, but all acoustic guitars share a similar anatomy. To begin, the lining affects the tone and structural stability of the acoustic guitar as it offers stability from vibrations 5 The unique bolt on the neck system offers the idea of replacing the neck and is debated to give an increase in tone 6. The most important part of a guitar is arguably the brace. Bracing is used to provide support and stability against the soundboard warping due to the tension of the strings. Furthermore, it helps transfer the vibrations of the strings to the soundboard.  Ideally, the bracing on the acoustic guitar transfers all the oscillation of the strings to the entire soundboard. During the mid 1800s, Antonio Torres of Spain established a fanned bracing pattern on his nylon string acoustic guitars, to stop his sound board from warping after plucking the nylon strings. Torres’ bracing pattern demonstrated sufficient strength to the soundboard of the guitar to counteract minor warping, and enhance the tone of the instrument dramatically. Torres’ bracing pattern has remained one of the most common bracing techniques on classical guitars to this day 7. Figure 3 8 (below-middle) shows the Torres bracing pattern. By the early 1900s,  steel guitar strings began to become available as attractive alternatives to nylon string. They offered louder volumes than nylon strings. Torres’ bracing pattern was sufficient for nylon strings; however, increased tension of the steel strings was too high and caused the soundboard to warp to a high degree. To take care of this, guitar manufacturers began using an X bracing pattern, which provided more support for the soundboard from warping. Christian Martin who established a company called C.F. Martin guitars in the 1830s, was an innovator of the X bracing pattern 9. Figure 4 10 (below-right) shows Martin’s X bracing pattern that is still widely used among many steel string guitars in the 21st century.FIGURE 2 4                         FIGURE 3 8                                   FIGURE 4 10                                           DIAGRAM OF THE PARTS OF A GUITARTo understand how a guitar works, one must first understand how sound behaves. Sound travels in the shape of a wave. There are two types of sound waves, longitudinal and transverse 11. Longitudinal waves travel parallel to the source of the wave and transverse waves travel perpendicular to the source of the wave. Sound is produced from vibrations through a medium, and travels in the form of longitudinal waves 12. Pitch is the general perception of the highness or lowness of a sound which depends on the frequency complexity, and loudness of the sound 13; on the other hand, in music pitch related to notes that are being played. The vibrations caused from a disturbance such as a vibrating string create areas of compression and rarefaction of the molecules in the medium that the vibrations are traveling through. Sound is only produced when these vibrations are traveling through a medium. An observer is able to hear sounds because these areas of compression and rarefaction are picked up by the observer’s ears, and translated to the brain from longitudinal sound waves. Figure 5 14 (middle-left) shows the areas of compression and rarefaction in the air in a hollow tube caused by the vibrations from a tuning fork. Compressions are areas of with a high density of molecules; whilst, rarefactions are areas with a low density of molecules.  Sound has many mathematical insights which apply to a guitar. There are two different kinds of acoustic guitars: classical and folk 15. The main difference between a classical and a folk guitar is the type of strings used. Classical guitars use nylon strings and folk guitars use steel strings. Furthermore, both types of guitars are tuned to the same frequencies; however, the nylon strings have a much lower density than steel strings, therefore the tension on the soundboard of the guitar is much less for a classical guitar than a folk guitar. Hence, the structure for the bracing  for a steel string guitar must be much stronger than the bracing of a classical guitar in order to handle the increased force on the soundboard due to the steel strings. When a note is played on the guitar, the string vibrates back and forth producing a wave. An acoustic guitar has six strings, each one of them has a different thickness and are tuned to a different frequency. The strings must be of different thicknesses because the velocity of a wave on the string depends on the tension, and the linear mass density of the string, shown in (2), where V is the velocity, T is the tension and L is the linear mass density. Thicker strings have a lower frequency, and the thinner strings have a higher frequency, due to the fact that thicker strings have a higher linear mass density, which reduces the velocity of the wave on the string for a given tension, and the result is a lower frequency. Linear mass density is expressed in (3), where M is the mass of the string and is the length of the string.V=(2)            µ=M/L(3)Whether or not a guitar is strung with nylon or steel strings, the frequency of the strings, and/or the frequency produced when a string is not fretted, is not changed. The velocity will change based on the size of the instrument. For any given frequency, a long wavelength means a lower velocity, and a short wavelength means a higher velocity. The strings on all guitars in standard tuning are tuned to the same frequencies, despite the length of the strings. Small guitars are tuned to the same frequencies as larger guitars. Table 1 shows the pitch as well as the frequencies of a guitar in standard tuning. TABLE 1 16                                                    GUITAR STRING NOTES AND FREQUENCIESIn order to change the note being played, the player must change the wavelength of the string by shortening the length of the string with their fingers. The velocity of the wave on the string remains constant, and by shortening the length of the string the frequency increases 17. The first harmonic, or the fundamental, shown in Figure 6 shows the motions of a plucked open string, which is half the wavelength of the wave on the string. This is known as the first harmonic. A harmonic is a signal or wave whose frequency is an integral (whole-number) multiple of the frequency of some reference signal or wave 18. The second harmonic is formed on a guitar by creating a node at the twelfth fret and is twice the frequency of the open string. Creating a node at the fifth or seventeenth fret forms the third harmonic and the frequency is three times higher than the open string 19.           There are two different phenomena that make the conversion of the mechanical energy from the player plucking a string to sound energy more efficient.  First, when the string vibrates above the sound hole of the guitar, the vibrations of the strings create areas of compression and rarefaction in the air around the sound hole. These vibrations compress the air inside the body of the guitar, which raises the internal pressure. The air is then forced out due to the high pressure. This is referred to as Helmholtz resonance. The vibration of the air inside the body of a guitar mostly affects the lower frequencies, so a guitar with a smaller body would produce softer low frequencies. This becomes apparent when looking at the violin family of instruments. The lower pitched instruments such as the cello or bass have larger bodies than the violin of viola. The other way that a guitar converts the mechanical energy to sound energy is through the vibration of the top of the guitar. The top or soundboard is designed to vibrate, and because of its large surface area, the vibrations move more air than the string alone could. The vibrating soundboard is an example of forced vibrations. The strings vibrate against the bridge, which forces the soundboard to vibrate. The soundboard projects the higher frequencies of a guitar into the air around the guitar. The more surface area of the soundboard, the louder the produced frequencies are 13. The combination of the low frequencies projected from the vibration of the air inside the body of the guitar as well as the high frequencies projected from the vibration of the soundboard gives the guitar its unique sound.If you were to take a guitar string (steel or nylon) and stretch it to a any length and a given tightness and have someone pluck it, you would hear a noise; however,  the noise would not even be close in comparison to the loudness produced by an acoustic guitar. On the other hand, if the string is attached to the sound box of the guitar, the vibrating string is capable of forcing the sound box into vibrating at that frequency. The sound box forces air particles inside the box into oscillation at the same natural frequency as the string. The entire system begins vibrating and forces surrounding air particles into oscillation. The tendency of one object to force another adjoining or interconnected object into oscillation is referred to as a forced vibration. In the case of the guitar string mounted to the sound box, the fact that the surface area of the sound box is greater than the surface area of the string means that more surrounding air particles will be forced into vibration. This causes an increase in the amplitude and thus loudness of the sound. 

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