An Analysis of Guitar Sounds

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Sound is defined as areas of high and low pressure that move outward to form a longitudinal wave. The amplitude and pitch of the sound is dependent on the source and amount of energy produced. Sound is produced by vibrating objects, the vibrations cause disturbances in the surrounding air molecules. When the vibrating object moves outward it causes the air molecules around it to compress and create a high pressure region. As the object moves inward the air molecules expand and create a low pressure region. The high pressure regions are called compressions and the low pressure regions rarefactions. The equation of sound waves is speed = wavelength x frequency or v = f x .

The instrument that will be analysed in this report is the acoustic guitar. An acoustic guitar is any guitar that uses acoustics as a means to transmit the strings vibrational energy to the air to produce a sound. The sound from an acoustic guitar is initiated by the strings. When plucked with the fingers or a plectrum it creates vibrational energy which is then transferred to the soundboard or soundbox. Without the soundboard the string alone would not be able to produce much sound as it would just cut through the air without causing much disturbance, but since the soundboard is large and flat it moves the air easier, this process is called mechanical impedance matching. This increases the systems energy transfer efficiency and produces a much louder sound.
All of an acoustic guitars components have a purpose and in some way contribute to the overall sound produced by the guitar. The headstock holds the tuning machines, which are geared mechanisms used to raise and lower the tension of the strings. A string with a higher tension will produce a sharper pitch...

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... for the fundamental frequency should equal twice the length of the guitar string.

The second harmonic is the fundamental frequency with an added node and antinode. The node is placed in the middle so that it creates an equal repeating pattern, so the anti-nodes are placed between the three nodes to keep an alternating pattern of nodes and anti-nodes. The third harmonic then has four nodes and three anti-nodes. The table below shows the number of antinodes, nodes, waves and string length to wavelength relationship for the first five harmonics.
Harmonic # # of Waves in Strings # of Nodes # of Anti-Nodes Length – Wavelength Relation
1 1/2 or 0.5 2 1 Wavelength = ½ String Length
2 2/2 or 1 3 2 Wavelength = String Length
3 3/2 or 1.5 4 3 Wavelength = 1 ½ String Length
4 4/2 or 2 5 4 Wavelength = 2 String Length
5 5/2 or 2.5 6 5 Wavelength = 2 ½ String Length

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