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All instruments of the various types all deal with the same general theories of sound. Sound travels through waves, and these waves transfer energy. No matter is transferred in this process. Known as mechanical longitudinal waves, the sound requires a medium to travel through while the motion is longitudinal. Essentially, particles move through the medium of air while all motion in the process is parallel. Waves can be measured in a number of ways, via wavelength, periods, or frequencies. Frequency is measured in Hertz, and is vibration. Sound waves differ from matter in that two or more waves can be in the same place at the same time. While both waves affect the medium in a different way these effects can be observed in what is commonly known as the superposition principle. The superposition principle says that the displacement of a medium of any medium caused by multiple waves are all of those added together.
Constructive interference occurs when the waves blend together to form a displacement farther from this equilibrium of these waves, destructive interference moves the equilibrium so that it lessens or becomes null. The loudness we hear for any musical instrument or any sound is more commonly referred to as intensity, while scientifically this can be found directly using the energy, time, and area. Mathematically this equates to intensity being the energy divided by the time multiplied times the area. Another way of considering this is intensity equaling the power divided by the area. Normally the units for measuring sound intensity are watts over meters squared. The human ear has the capability of hearing very low intensities (while animals such as dogs, however, can hear very high intensities.) The intensity can also be considered as the pressure wave in which a compression of particles of a medium raise the pressure of the air within this region to.3 billionths of an atmosphere (Mr. Fizzix). Harmonics, also known as overtones, are the frequencies of waves and tones, and are especially relevant to string instruments.
The specific frequencies selected for the musical scale are not selected at random for any instrument. Most strings sound good when struck in conjunction. Specific pitches and tones sound pleasurable because they are chosen with regards to some predetermined scale. In a modified piano, the keys represent diatonic scales, while some are assigned to low frequencies while others are assigned to higher ones. Sharp and flat notes are also represented while a number of other notes represent the full chromatic scale. The frequency of the sound make by all of the keys is this chromatic scale. While the opposite of dissonance is consonance, we experience a blend of harmonious frequencies across a range of hertz. Tuning forks operate in the same manner while replacing a 400 Hz fork with a 850Hz one, a fantastic example of consonance would be heard. The usual harmony in this case is explained by the fact that each crest in the wavelengths for the sound wave made by the fork are aligned with each other. In this, the doubling of frequency for one tone will thus create a second tone each time which will sound pleasant in combination with the first. The Greek culture was aware of this fact, and thus implemented it in many ways (Lapp).
With regards to a created instrument, we will discuss the applications and theory in a three-stringed guitar. Consider that the easiest way for a string to vibrate is with each end bound while the middle is plucked, and the result is a vibration across two equal segments. This is commonly called the first mode, while more complicated ways of doing this are referred to as second and third mode, etc. With this in mind we can consider the variety of relevant aspects in the rest of the theory. Wave speed in strings is dependent upon two factors, the density of the linear mass (e.g. the composition of the string itself) and the tension in the string.
The tension can be adjusted in any well crafted instrument or can at least be created to some precision in the creation of a homemade instrument. It takes more force to pluck a string with very high tension than it does to pluck a string with very low tension. More force applied to a tense string in this case is followed by a reduced period of restoring equilibrium due to the tension. As a result, more tension causes a quick response, and thus, an overall higher value for the velocity of the ending wave (Lapp). The wave velocity is also proportional to other values, such as the density of the physical string. The higher this value is, the higher the total mass is, which results in a higher resistance to change or inertia, which then results in a slower response from being plucked and a reduced wave velocity. Tension and density thus have opposite effects.
Acoustic and electric guitars have different theory relevant to them. It would be possible to further the creation of the three-stringed guitar to an electric guitar, though this would obviously require a lot more work from a physics lab type of environment (due to the obvious need for electrical components.) The electric guitar uses a different method for amplifying, based on electromagnetism. Electromagnetism plays no role in acoustic guitars. In the electric guitar, there are electromagnetic ‘pickups’ which are composed of a magnetic core and coils of wire. These change the flux of the field passing through, while converting it into a signal which then can be heard from the speaker. Strings do not require any coupling to a soundboard, as acoustics require, so they can vibrate for a longer period of time (Lapp).
Electric guitars are more commonly associated with European and American cultures. While they are used across the world, there is apparently more hype at least with guitar users in these nations. While the invention is somewhat new, there is no native of ancient cultural link (Summersfield). The original guitars are thought to have evolved as long as 5000 years ago, although there is naturally less certainty with increasing age. Spanish guitars during the Renaissance period become quite popular, while they were also known to be in use during 40AD in Rome. Modern guitars are known to have been manufactured around 1790, while claims of modern guitars existing before then are disputed (Tyler). Overall, the guitar is a very popular instrument which is used in many countries across the world, however. Other cultures may follow the American and European trends and develop a more popularized use. While there is much theory involved in strings, the applications are nearly limited by practicality. The dimensions for any of these can be changed to suit any situation, while these instruments continue to be used across the world.
Lapp, David, The Physics of Music and Musical Instruments, Tufts University, 2003.
The Physics of Musical Instruments. By Mr. Fizzix, Web.
Summerfield, Maurice J,The Classical Guitar, It’s Evolution, Players and Personalities since 1800 (5th ed.), Blaydon on Tyne: Ashley Mark Publishing, 2003.
Tyler, James,The Guitar and Its Music: From the Renaissance to the Classical Era by James Tyler, 2002.