The Physics of Stringed Instruments
Physics is a science that can be applied to anything. It can explain how sound is made and how it can be manipulated. This paper will explain how musical instruments, stringed instruments in particular, create the music that is part of all of our lives. There are many different types of musical instruments and many different ways to play them. They are each constructed in diverse ways to produce various sounds. Their strings are their most important part and can be created and played in different ways to create diverse sounds. Stringed instruments are very intricate and all of their many facets can be related to physics.
Stringed instruments, such as the violin family and the acoustic guitar, have many of the same parts. These include the body, bridge, sound hole(s), neck, fingerboard, nut, head, tuners, and strings. The body is made out of wood and is hollow. On a guitar, it has a circular sound hole in its center, while on a violin, it has two f-holes, named for their shape, on both sides of the bridge.
These holes allow air to move in and out of the body, therefore allowing sound to move out more effectively and they also allow the wood to vibrate different ways, therefore allowing more frequencies to emit. Inside the body there are two pieces of wood. One, called the soundpost, connects the top and bottom of the body. It vibrates and also prevents the top of the instrument from imploding. It is placed under the left leg of the bridge. Under the right leg is the bassbar. This is a piece of wood running up and down the instrument. It is there to vibrate and produce more overtones. The bridge sets the length of the strings as well as placing them at the proper height and connecting them to the body, allowing vibrations to enter and produce more sound.
The strings have to be above and not touching the fingerboard because if they were to touch, the string would be shortened and an unwanted note would be played. This is also accomplished by the nut, which is a piece of wood at the top of the fingerboard, supporting the strings. The bridge on a guitar holds the ends of the strings in place, while on a violin, the strings just go over the bridge and are held in place by the tail piece which is at the bottom of the instrument.
The neck is an extension of the body. It is not hollow and extends from the top of the body to the head. It supports the fingerboard which creates a surface for the strings to be pressed down on to make them shorter. On a violin, it is smooth, but on the guitar it has frets. Frets are bands of metal placed across the fingerboard lengthwise. When the string is pressed down in between two frets, the note of the lower fret is played. Frets are placed so that each consecutive one plays a note higher.
The head is at the top of the instrument and holds the tuners. It is called the pegbox in a violin as it holds the pegs which the strings are wrapped around. By turning the pegs, the strings become tighter or looser and change frequency. A guitar uses mechanical turners, not pegs. These are turned and change the pitch of the string up or down depending on the tension. Last but definitely not least, there are the strings. These are usually made of metal and run from the bridge in guitars or the tailpiece in violins to the head of the instrument. They are usually made from a metal wire with a smaller wire wound around it to make on wound string but can also be made from animal gut. Stringed instruments are very intricate, but all of these parts combine to create great finished products.
The main things that make two sounds different from each other are their frequencies. The frequency of a sound wave, also called its pitch, is the number of waves in one second. Its equation is where is the period and f is the frequency. It is measured in Hertz(Hz). Different frequencies produce different notes. Notes are letters assigned to a frequency and all its multiples. The table to the right starts at middle C (C4) and ends at another C (C5) an octave up. It also includes standard A which has a frequency of 440Hz.
The numbers next to the notes are their octaves above the beginning of the audible range. Notes can be arranged in scales and chords. Scales are a sequence of notes. Common types of scales are diatonic, chromatic, pentatonic, hexatonic, and heptatonic. A diatonic scale contains seven notes. Five separated be whole steps and two by half steps. A whole step is moving two notes up the table at right. An example would be going from D to E. A half step is moving one note up the scale. This would be from F to F#. The # stands for sharp and the b stands for flat. These are notes in between two notes, however, not all notes have sharps and flats such as B and C, there is not B# or Cb. A chromatic scale has twelve notes, each going up by half steps. Pentatonic, hexatonic, and heptatonic have five, six, and seven notes, respectively.
The strings of a stringed instrument are its most important part. They are the source of the music and are how the instrument is played. There are four strings on the violin and six on the guitar. The strings go have different pitches. This is created by giving the string different masses. The more mass a string has, the lower it vibrates, therefore producing a lower frequency.
This was shown in the spring lab in which a more dense spring was attached to a less dense spring. The wave sent through them moves quicker through the less dense spring. The less dense spring had a higher frequency. Two other factors can change the frequency. These are tension and length. The tension of the string is changed during tuning to create the desired sound. The more tension, the higher the string’s frequency is. The length of strings is changed constantly while playing. When you put your finger down over a string, it shortens it, making the string sound at a higher frequency.
The guitar has its strings tuned, from lowest to highest, at E, A, D, G, B, E. The guitar is tuned in perfect fourths which essentially means that the strings are five half steps apart. This can be shown by a piano keyboard; a fourth is moving three white keys up the piano. There is however one anomaly on the guitar as the change from the G to the B string is a third, not a fourth. The violin is tuned in fifth which is basically the inversion of tuning in fourths and the strings are seven half steps apart. The strings go, in order from lowest to highest, G, D, A, E. If you compare the violin strings with the guitar’s, you will see that the violin’s strings are the four lowest strings of the guitar backwards.
A fifth can be shown on a piano by playing a note, then counting four white keys up and playing that note. If you notice, while playing fourths or fifths, they sound good together. This is due to consonance. Consonance is when two notes sound good together in harmony. Both fourths and fifths are good examples of consonance. Another example of consonance is harmonics. Harmonics are essentially standing waves. They split up the string into standing waves, the higher the harmonic, the more standing waves. Using standard A at 440Hz, its first harmonic is at 440Hz, its second is at 880Hz, its third is at 1320Hz, and its fourth is at 1760Hz. The pattern continues past this point. As shown by their names, stringed instruments’ most significant parts are their strings.
As you can see, stringed instruments have many different parts and are related to physics in many ways. Their strings display different frequencies by their masses, tension, and length. They are designed to vibrate the air around them to better play their sounds. Musicians use consonance, harmonics and the aforementioned properties to play music on these instruments. Stringed instruments are one of the most complex and widely used instruments to ever be created. [Creative Commons Copyright]
Works cited
http://www.phy.mtu.edu/~suits/Physicsofmusic.html
http://www.phy.mtu.edu/~suits/notefreqs.html
http://www.tufts.edu/as/wright_center/physics_2003_wkshp/book.htm
http://www.phys.unsw.edu.au/music/
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