Vibration, standing waves in a string, The fundamental and the first 6 overtones which form a harmonique serie

A vibration in a string is a wave. Usually a vibrating string produces a sound whose frequency in most cases is constant. Therefore, since frequency characterizes the pitch, the sound produced is a constant note. Vibrating strings are the basis of any string instrument like guitar, cello, or piano. It should be emphasized that this article's content is theoretical in nature, to be enhanced with actual observation. Image File history File links Metadata Size of this preview: 576 × 599 pixelsFull resolution (6064 × 6309 pixel, file size: 1,016 KB, MIME type: image/jpeg) This is image is made by me and everybody is allowed to use it. ... Image File history File links Metadata Size of this preview: 576 × 599 pixelsFull resolution (6064 × 6309 pixel, file size: 1,016 KB, MIME type: image/jpeg) This is image is made by me and everybody is allowed to use it. ... Vibration and standing waves in a string, The fundamental and the first 6 overtones A standing wave, also known as a stationary wave, is a wave that remains in a constant position. ... A fundamental is something that cannot be built out of more basic things, which other things are built upon. ... Approximate harmonic overtones on a string An overtone is a natural resonance or vibration frequency of a system. ... See Harmonic series (music) Harmonic series (mathematics) These two concepts are related. ... Look up vibration in Wiktionary, the free dictionary. ... The strings of a harp A string is the vibrating element which is the source of vibration in string instruments, such as the guitar, harp, piano, and members of the violin family. ... A wave is a disturbance that propagates through space or spacetime, transferring energy and momentum and sometimes angular momentum. ... Sound is a disturbance of mechanical energy that propagates through matter as a wave. ... For other uses, see Frequency (disambiguation). ... Pitch is the perceived fundamental frequency of a sound. ... A string instrument (or stringed instrument) is a musical instrument that produces sound by means of vibrating strings. ... For other uses, see Guitar (disambiguation). ... The violoncello, usually abbreviated to cello, or cello (the c is pronounced as in the ch of check), is a bowed stringed instrument, a member of the violin family. ... A short grand piano, with the top up. ...

Speed of propagation of the wave

Let L be the length of the string, m its mass and T the tension. Image File history File links Illustration for vibrating strings. ... For other uses of this word, see Length (disambiguation). ... This article or section is in need of attention from an expert on the subject. ... Tension is a reaction force applied by a stretched string (rope or a similar object) on the objects which stretch it. ...

When the string is deflected it bends as an approximate arc of circle. Let R be the radius and θ the angle under the arc. Then . Circle illustration This article is about the shape and mathematical concept of circle. ... Remote Authentication Dial In User Service (RADIUS) is an AAA (authentication, authorization and accounting) protocol for applications such as network access or IP mobility. ... This article is about angles in geometry. ...

The string is recalled to its natural position by a force F: its made by jaypeeng magandang google wikepedia For other uses, see Force (disambiguation). ...

The force F is also equal to the centripetal force The centripetal force is the external force required to make a body follow a circular path at constant speed. ...

where v is the speed of propagation of the wave in the string.

Let μ be the linear mass of the string. Then This article does not cite any references or sources. ... Linear mass is a measure of mass per unit of length, and it is a characteristic of strings. ...

and

Equating the two expressions for F gives:

Solving for velocity v, we find

Frequency of the wave

Once the speed of propagation is known, the frequency of the sound produced by the string can be calculated. The speed of propagation of a wave is equal to the wavelength λ divided by the period τ, or multiplied by the frequency f : For other uses, see Frequency (disambiguation). ... Sound is a disturbance of mechanical energy that propagates through matter as a wave. ... This article does not cite any references or sources. ... The wavelength is the distance between repeating units of a wave pattern. ... Periodicity is the quality of occurring at regular intervals (e. ... For other uses, see Frequency (disambiguation). ...

If the length of the string is L, the fundamental harmonic is the one produced by the vibration whose nodes are the two ends of the string, so L is half of the wavelength of the fundamental harmonic. Hence: Vibration and standing waves in a string, The fundamental and the first 6 overtones The fundamental tone, often referred to simply as the fundamental and abbreviated fo, is the lowest frequency in a harmonic series. ... A standing wave. ...

where T is the tension, μ is the linear mass, and L is the length of the vibrating part of the string. Therefore: Tension is a reaction force applied by a stretched string (rope or a similar object) on the objects which stretch it. ... Linear mass is a measure of mass per unit of length, and it is a characteristic of strings. ... For other uses of this word, see Length (disambiguation). ...

• the shorter the string, the higher the note
• the higher the tension, the higher the note
• the lighter the string, the higher the note

Observing string vibrations

One can see the waveforms on a vibrating string if the frequency is low enough and the vibrating string is held in front of a CRT screen such as one of a television or a computer (not of an oscilloscope). This effect is called temporal aliasing, and the rate at which the string seems to vibrate is the difference between the frequency of the string and the refresh rate of the screen. The same can happen with a fluorescent lamp, at a rate which is the difference between the frequency of the string and the frequency of the alternating current. (If the refresh rate of the screen equals the frequency of the string or an integer multiple thereof, the string will appear still but deformed.) In daylight, this effect does not occur and the string will appear to be still, but thicker and lighter, due to persistence of vision. Temporal aliasing is the technical term for a phenomenon also known as the stroboscopic effect or the wagon-wheel effect. ... According to the theory of persistence of vision, the perceptual processes of the brain or the retina of the human eye retains an image for a brief moment. ...

A similar but more controllable effect can be obtained using a stroboscope. This device allows the frequency of the xenon flash lamp to be exactly matched to the frequency of vibration of the string; in a darkened room, this clearly shows the waveform. Otherwise, one can use bending to obtain the same frequency, or a multiple of, the AC frequency to achieve the same effect. For example, in the case of a guitar, the bass string pressed to the third fret gives a G at 97.999 Hz; with a slight bend, a frequency of 100 Hz can be obtained, exactly one octave above the alternating current frequency in Europe and most countries in Africa and Asia. In most countries of the Americas, where the AC frequency is 60 Hz, one can start from A# at 116.54 Hz, on the fifth string at the first fret, to obtain a frequency of 120 Hz. A stroboscope , also known as a strobe, is an instrument used to make a cyclically moving object appear to be slow-moving or stationary. ... Xenon flash lamp being fired. ... Example of bending on electric guitar A bend is a guitar technique that involves bending the tone upwards, thus making the note or chord sound sharper than normal. ...

See also

• String instruments
• Fretted instruments
• 3rd bridge guitar
• Physics of music
• Musical acoustics
• Pitch
• Franz Melde

A string instrument (or stringed instrument) is a musical instrument that produces sound by means of vibrating strings. ... The neck of a guitar showing the first four frets. ... It has been suggested that this article or section be merged into Prepared guitar. ... Sound waves Variations in air pressure against the ear drum, and the subsequent physical and neurological processing and interpretation, give rise to the experience called sound. Most sound that people recognize as musical is dominated by periodic or regular vibrations rather than non-periodic ones (called a definite pitch), and... This article or section does not cite its references or sources. ... Pitch is the perceived fundamental frequency of a sound. ... Franz Melde was a German physicist (born March 11, 1832 - died March 17, 1901). ...

References

• Molteno, T. C. A.; N. B. Tufillaro (September 2004). "An experimental investigation into the dynamics of a string". American Journal of Physics 72 (9): 1157-1169. 
• Tufillaro, N. B. (1989). "Nonlinear and chaotic string vibrations". American Journal of Physics 57 (5): 408. 

External links

• Java simulation of waves on a string
• Physics of a harpsichord string
• A study of chaotic motion in strings