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The Physics from the Electric Bass

A song's harmony and rhythm are greatly enhanced through the addition of an electrical bass. Many people don't realize its function, but merely removing it from the musical base reveals the way the outcome is a song devoid of emotion and sound. Past the really low timbres, that provide color and feeling to the music, the electric bass provides many insights into physics and mathematics, which must be observed and studied cautiously.

Natural vibrations

Any sound is generated by a vibration. Every object that vibrates emits a sound, whether it's a bell, a string, a drum, or a bit of metal. Even the wind, if properly channeled, can produce a sound.

Every object vibrates at its very own natural speed, which is called the \”natural frequency.\” The human ear can hear only vibrations that occur at a speed between 20 Hz and 20,000 Hz. Slower or faster ones can be heard only by animals and special acoustic sensors. The pitch of a sound is measured in hertz, which counts the number of oscillations per second. Note A (A) above middle C around the piano has a frequency of 440 Hz, as the same note around the electric bass string is three octaves lower (55 Hz). The frequency halves for every octave lower, although it doubles for every octave higher.

The electric bass

An electric bass looks like an electrical guitar, nevertheless its functionality is different. It's a stringed guitar that generates sounds with very low and engaging frequencies. It performs a rhythmic and harmonic function simultaneously. This information will not, of course, cope with the musical facets of the instrument, but it will delve into concepts that fall inside the field of physics. The bass guitar might have four, five, or six strings, but the most typical instrument has four strings, consists of stainless or nickel, and is the amplified instrument analogue from the double bass. The tuning of the four-string electric bass is really as follows, starting with the biggest string:

  • Note E (E): 41.20-Hz frequency
  • Note A (A): 55.00-Hz frequency
  • Note D (D): 73.42-Hz frequency
  • Note G (G): 98.00-Hz frequency

Figure 1 shows the graphical spectrum of the frequencies generated by the four strings from the electric bass guitar. The sounds are generated by plucking the strings. As can be seen, the spectrum isn't perfect, and there's the existence of some higher harmonics. It is because the instrument's metal strings are not capable of establishing a perfect sinusoidal signal. But this truth is not synonymous with imperfection, and also the waveforms generated by the instrument contribute to the characteristic sound from the electric bass.

Musical notes are managed by mathematics

Mathematics and music appear to be two separate fields, the former using the brain and the latter using the heart. Instead, mathematics also seems to go into the field of music. Any events that regulate frequencies, rhythms, timings, and note types are organized together in many mathematical laws (begin to see the graph in Figure 2). A persons auditory system can decode sound signals only inside a narrow frequency range of 20 Hz to 20,000 Hz (audible band). Outside this window, it cannot hear anything. There is a close relationship between your frequencies of sounds and their musical notes. If one imagines a scale of semitones between Note C (musical octave # 1) of 16.35 Hz and Note B (musical octave number 9) of seven,902.13 Hz, a precise exponential mathematical relationship exists:

where a may be the constant 15.4338, b may be the constant 1.0594, f may be the frequency to be calculated, and x may be the order quantity of the note. (For example, Note A has got the numbers 10, 22, 34, 46, 58, 70, 82, 94, 106, etc.).

Another interesting relationship makes it possible to calculate the frequency of the other notes by understanding the frequency of Note A from the reference octave:

where f_rif is the frequency of Note A of the reference octave and N may be the quantity of semitones from the reference note.

The first formula is, obviously, more general and adaptable to any context. It generates the frequencies listed in the next table, simply supplying the sequential order number of the note, between 1 and 120.

The tuning of the electric bass

The tuning from the four strings from the electric bass guitar is the same as that of the first four strings of the guitar and includes the pitches E (E), A (A), D (D), and G (G), respectively. The particularity of the tuning is that the four notes are identical musical interval apart (see Figure 3). But there's another peculiarity in electric bass tuning. The number of the regularity of one string to that particular from the next string is definitely comparable to the continual:

In other words, any jump, interval, and chord configuration could be set on any string and it is exactly the same for those strings. These functions make the bass player's job somewhat easier. During tuning (see tuners in Figure 4), tension is used to the strings before the exact note is reached. The strings are constructed to resist great tension. The vibration of the string occurs in a certain frequency because after it is plucked, it is fixed at two ends, represented through the bridge and the capo. In years past, tuning was done by ear, however this was difficult due to the low frequencies involved. Later, acoustic tuners were built, which took the audio signal directly from the pickup from the electric bass and sent it towards the measuring instrument. Only recently have particular tuners been developed that may sense the mechanical vibrations of the neck and show the end result on the display. They're very convenient because along with their inherent precision, they are able to carry out attentiveness a really noisy and acoustically disturbed environment. In any case, individuals with an electronics lab can carry out tuning with an oscilloscope or a good frequency meter.

Good tuning depends very much around the physique from the instrument and the kind of static and dynamic materials used (wood, strings, metal, etc.). The physical type of the electric bass can also be of fundamental importance, specially in the physics of vibrations and resonances. Whether or not the instrument is not acoustic but electric, some unwanted resonances could be revealed that could drastically alter the sound picked up through the pickups (see simulations in Figure 5). The phenomenon of resonances, harmonics, and vibrations is much more evident in acoustic instruments, plus they cause real transient deformations, obviously in the order of thousandths of the millimeter. These natural frequencies (called Eigen frequencies) are discrete frequencies at which the machine is predisposed to vibrate. When it vibrates in a certain natural frequency, the dwelling deforms. Under certain conditions, a string starts to vibrate autonomously when there are other soundwaves of similar frequency in the vicinity. The string begins to vibrate without being plucked or touched. The acoustic sound vibrates the string through the air. The entire system therefore vibrates at the same frequency. This phenomenon is known as resonance.

An interesting effect that may be made up of the electrical bass (but additionally using the guitar) is harmonics. Natural harmonics are sounds that can be made by developing a knot, through slight pressure (almost a grazing) at certain precise points around the vibrating string, the following:

  • In the middle of the string, in the 12th fret
  • At one-third of the string, at the seventh fret
  • At one fourth from the string, at the fifth fret
  • At one-fifth of the string, at the fourth and ninth frets

Natural harmonics can be used to create chords, with very striking musical effects.

A simple electric bass amplifier

Commercial amplifiers really are a gold mine of technology when it comes to the reproduction of low frequencies. A great electric bass amplifier should hold the following minimum characteristics:

  • The existence of a subwoofer with a diameter of at least 10 inches
  • A bandwidth from 0 Hz to 200 Hz
  • Possibility of adjusting the different tones
  • High power and protection against high peaks

In nevertheless, for small home reproductions, the circuit diagram reproduced in Figure 6 is much more than sufficient. It's designed with the LM386 integrated circuit for low-voltage operation. Automatically, the gain is set internally to 20, but the addition of an external resistor along with a capacitor between Pin 1 and Pin 8 provides the possibility of adjusting the gain to the value between 20 and 200. The inputs are referenced to ground, as the output is automatically biased to half the supply voltage, which must be between 4 V and 12 V DC. The configuration adopted within the circuit diagram improves the low-frequency notes.


Music encapsulates many concepts in physics and mathematics. Vibrations, frequencies, periods, musical notes, perturbations in mid-air, special effects, and many more could be contemplated in such art. The study of the physical and mathematical laws that bind and describe the different laws assists you to know the entire behavior of the system so that all of its characteristics could be controlled and it is behavior predicted.