The due to the height the string changes

The first guitar designed to beelectrically amplified was created in 1931 by George Beauchamp, and was ahollow body guitar that utilised a tungsten pickup, see Fig1. This was a one-piececast aluminium body and utilised electromagnetic transducers. Considered by mostto be the known as the “frying pan”, created by George for Rickenbacker Electro    Guitars1. This guitar utilised all the features common to modern dayelectric guitar such as potentiometers to control volume and treble, andmagnetic pickups to send the signal to an amplifier.

Something to consider with theguitar is the range of pitches available to a player. For a standard six stringmodel, the lowest note is the low E, at 82.41Hz and the highest is the high E,4 octaves above this, at 1320Hz. However, guitarists can change the pitch of anote by applying more tension to the string through bending the string,allowing a high G to be reached at 1568Hz.

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However, for guitars over 6 stringssuch as those up to 8 or 9 strings, the lowest note can be as low as 36.7Hz,which is almost below the point of human hearing. When changing the pitch of anote, the guitarist must apply varying degrees of force at different originalpitches to change the note to the desired pitch, depending on where they areplaying the note on the neck. This is due to the height the string changes whenit is pushed onto the frets of the fretboard, see Fig 2, the closer the fret isto either the nut or bridge of the guitar, the locations where the string ends,the longer the overall string shall become.

This means that to bend to pitch atfrets closer to either the bridge or nut, greater pressure must be applied toreach the same change in pitch.Whileplaying a note, one of the main differences between a guitar and almost everyother type of instrument is the ability to play achromatic notes, notes whichare outside the established Western scales. This is due to the ability to benda string and apply vibrato, which is when the length of the string is subtlychanged with a regular such that the pitch is shifted slightly out of thechromatic range established by Western scales, allowing a continuous range ofpitches to be reached as opposed to the discrete range which is possible from mostinstruments.Different pitches are achieved onthe guitar in several ways. One of which is the scale length, which is brokenat 21, 22 or 24 places by frets.

Each of these frets is located in amathematically calculated place, so that the correct pitch can be achieved. Theformula used for this isThis recursive formula shows that,for a typical guitar of scale length, distance between the nut and brige,25.5″, the first fret is at 1.431″, the second at 2.782″, the third at 4.057″and so on. The value of 18 used to be used, referred to as the “rule of 18” butby further refinement this has been narrowed down to 17.817 5, knownas the equal temperament constant.

Inthe same way as for other stringed instruments, it is simple to work out thelowest harmonics available on the guitar. We can do this by considering astanding wave on the guitar. As it is a closed string, we must have a minimumat each end, so the largest wavelength available for the string is twice thelength of the string, with the second being the length of the string and so on,following the formulaThe key thing that differentiatesthe electric guitar from an acoustic guitar is the magnetic pickup. A pickup iscreated by coiling a metal with a high intrinsic magnetic moment around 6 permanentmagnets roughly 5 to 10 thousand times, creating a dynamo. Themagnets in the pickups cause the portion of the strings above them to becomemagnetised and thus to produce a magnetic field. Therefore, when the stringvibrates after being plucked, the string vibrates with a certain frequency andtherefore so does the magnetic field generated by it.

This changes the fluxthrough the coils of the pickup, so the rate of change of the flux is non zero.The induced potential difference is caused by the electromotive force, describedby:When the string vibrates above thepickup, it generates a potential difference which, when the guitar is pluggedin and makes a complete circuit, creates a voltage and current flows to theamplifier, allowing for amplification of the note. The pickup is either onecoil, or two coils wired in series but placed in opposite polarities, known asa humbucker. This humbucker design was created by Gibson and the patent wasapplied for on June 22nd, 1955 6. The design wasnecessary as single coil pickups are very effective at picking up frequenciesof 50 Hertz 7, frequencies produced by mains wiring, leading to adistinctive and irritating hum. As the level of electronic gain is increased, alayer of natural compressions is added which increases the volume of this humand leads to feedback loops when playing at high volumes.

The design of thehumbucker pickups deals with this by having each coil pick up the same amountof string vibration and background hum, meaning the voltages are added togetherbut the ratio of noise to signal is the same. However, as one coil is reversedrelative to the other, the signal produced by the vibrating string is unchanged,while the hum produced by the pickup receiving signals from radio sources andAC current nearby is reversed between the coils, which cancels out the hum inthe output of the pickup as a whole. In practise, as the two coils cannot be identical,not all hum is cancelled although the majority is. Usinghumbuckers, however, changes the “tone” of the guitar.

It does this for severalreasons. One of these is that, by utilising two coils, the total number ofturns is more, and a greater potential difference is generated by the vibratingstring. This results in the output having a higher amplitude, which, whenamplified by a valve amplifier, changes the tone. For example, the naturalcompression by the valves is increased by the greater strength of the inputsignal, resulting in a slightly more artificial sound. This natural compressionin valve amplifiers also results in a more pronounced bass end of the tone dueto the bass elements of the sound being relatively lower in presence, meaningthe sound will cut through a mix with greater difficulty and therefore will havea harder time being perceived by the audience. The compression has a thirdfactor to it as well; due to the signal compressions resulting in asymmetricclipping of the generated wave, distortion is generated by the amplifier. Thischange in sound is desirable for certain genres such as rock and metal wherehumbucker equipped guitars are predominantly used but for other genres such asfunk, this sound is not.

Therefore, most players in this genre will use lowoutput single coil equipped guitars to achieve the correct sound.After this, the signal travels throughthe circuit of the guitar, often through two potentiometers, one which controlsvolume and the other which controls tone. These work by reducing the voltage ofthe signal travelling through and therefore reducing the amplitude of thesignal. For the volume control this reduces the volume.

For the tone control,the processes are slightly more complicated. With this potentiometer, acapacitor is wired between terminal of the potentiometer and the ground, and asthe voltage is changed by the potentiometer, the capacitor acts as a highfrequency drain on the signal, by the formulaIn conclusion, the physics of the electricguitar are fascinating and allow it to produce a far wider variety of soundsthan most other physical instruments, rather than the technological, forexample by the ability to bend strings and apply vibrato to change the pitch ofa note subtly outside of the chromatic 12 interval Western scale structure. Inaddition to this, the pickups of the guitar, by converting the mechanical waveto an electrical signal by electromagnetic inductance, allow a guitar to beamplified and have analogue processing applied to the signal, resulting in aplethora of tones varying both in gain level as well as tonal structure andbalance. This is one of the reasons the guitar is one of the most playedinstruments on the planet.