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Topic: Vibrating string

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	The Vibrating String
		Tension in the string is supplied by weights on a weight holder attached to the end of the string hanging over the pulley.
		The mechanical vibrator should be attached near the fixed end of the string at a position that maximizes energy transfer to the string without constraining its motion.
		Measure the length of the string and weigh it.
	www.csudh.edu /wiley/phy132l01/wave.htm (910 words)

	Vibrating string
		Vibrating strings are the basis of any string instrument like guitar or piano.
		The string is recalled to its natural position by a force which is equal to.
		If the length of the string is, the fundamental harmonic is the one produced by the vibration whose nodess are the two ends of the string, so is half of the wavelength of the fundamental harmonic.
	www.casimiro.com /wiki/en/wikipedia/v/vi/vibrating_string.html (292 words)

	Harmony Central - Understanding Harmonics
		The pitch of a plucked string is dependent on three factors: the length of the string, the tension in the string, and the mass density of the string (i.e.
		Figure 1 shows a string vibrating where the length of the string is equal to a half-wavelength.
		First of all, play a fretted string and notice that the portion of the string between your finger and the nut is not vibrating.
	www.harmony-central.com /Guitar/harmonics.html (1933 words)

	Science Fair Projects - Vibrating string
		Let L be the length of the string, m its mass and T the tension.
		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.
		where T is the tension, μ- is the linear mass, and L is the length of the vibrating part of the string.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Vibrating_string (445 words)

	Response Effects of Guitar Pickup Position and Width
		The string "scale length", or distance between the nut and the bridge, is 25.5 inches.
		Figure 1 is the simplest case; the string is vibrating at the fundamental frequency on the "open" (or unfretted) string.
		As far as the pickup is concerned, the effects of the nodes and antinodes are due to the wavelength on the string and not whether the string vibration is a due to a fretted fundamental or a harmonic.
	www.till.com /articles/PickupResponse (3596 words)

	NationMaster - Encyclopedia: Initial condition
		For example when a vibrating string is modelled, we assume that the two ends are held fixed: this accords with physical intuition.
		With the function to be found representing the displacement as function of position on the string, this implies the solution should take the value 0 at two points through all time.
		Another example from this kind is a whip—a string held fixed at one end, with the other end free to vibrate.
	www.nationmaster.com /encyclopedia/Initial-condition (516 words)

	The Physics Classroom
		As the vibrating string moves in the reverse direction (leftward), it lowers the pressure of the air immediately to its right, thus causing air molecules to move back leftward.
		The back and forth vibration of the string causes individual air molecules (or a layer of air molecules) in the region immediately to the right of the string to continually move back and forth horizontally; the molecules move rightward as the string moves rightward and then leftward as the string moves leftward.
		Regardless of the source of the sound wave - whether it be a vibrating string or the vibrating tines of a tuning fork - sound is a longitudinal wave.
	www.physicsclassroom.com /Class/sound/U11L1b.html (474 words)

	String Thing (Site not responding. Last check: )
		"A through understanding of vibrating strings, its dynamic, its natural vibrations, its response at different frequencies - we are introduced to results and concepts that have their counterparts throughout the realm of physics, including electromagnetic theory, quantum mechanics, and all the rest." A. French.
		These "stationary vibrations", called this because each point on the string vibrates transversely in simple harmonic motion with constant amplitude, have the same frequency of vibration for all parts of the string.
		Example: The E string of a violin is to be tuned to a frequency of 640 Hz.
	www.lcse.umn.edu /specs/labs/string_page.html (535 words)

	T's Technical Notes
		The fundamental frequency, fr (in Hertz) of a vibrating string is a function of three fundamental factors.
		The string is made with an inner core and a small winding of nickel or bronze around it.
		As mentioned earlier, the low string on a guitar is the E3 note at 82.40689Hz; the high string on the guitar is two octaves higher (E5) or 329.6276Hz.
	terrydownsmusic.com /technotes/StringGauges/STRINGS.HTM (987 words)

	NOVA \| Elegant Universe \| Resonance in Strings \| PBS
		This is the string's fundamental resonant pattern, or frequency.
		With the strings in string theory, however, the vibrational pattern determines what kind of particle the string is. One resonant pattern makes it a photon, for example, while another makes it a heavy particle found within the nucleus of an atom.
		Although the fundamental string shown above is depicted as a two-dimensional object, the strings in string theory are one-dimensional.
	www.pbs.org /wgbh/nova/elegant/resonance.html (571 words)

	Classical Vibrating String
		The tangent to the string at y(x,t) is indicated in the figure; it forms the hypotenuse of a right triangle with legs parallel and perpendicular to the undisplaced string position.
		A uniform string under tension and of length L is displaced at its center a distance h and released from initial velocity zero.
		A uniform string with length L under tension is plucked at x = L/3 with an amplitude h and released.
	www.sci.wsu.edu /idea/quantum/Vibr_string.htm (1042 words)

	The Universe on a String A Unifying Theory - Science - RedOrbit
		And much as different vibrations of a violin string produce different musical notes, different vibrations of the theory's strings produce different kinds of particles.
		An electron is a tiny string vibrating in one pattern, a quark is a string vibrating in a different pattern.
		Crucially, the early pioneers of string theory realized that one such vibration would produce the gravitational force, demonstrating that string theory embraces both gravity and quantum mechanics.
	www.redorbit.com /news/science/702230/the_universe_on_a_string_a_unifying_theory/index.html?source=r_science (1547 words)

	NOVA \| The Elegant Universe \| A Theory of Everything? \| PBS
		String theory adds the new microscopic layer of a vibrating loop to the previously known progression from atoms through protons, neutrons, electrons, and quarks.
		String theory proclaims, for instance, that the observed particle properties—that is, the different masses and other properties of both the fundamental particles and the force particles associated with the four forces of nature (the strong and weak nuclear forces, electromagnetism, and gravity)—are a reflection of the various ways in which a string can vibrate.
		Just as the strings on a violin or on a piano have resonant frequencies at which they prefer to vibrate—patterns that our ears sense as various musical notes and their higher harmonics—the same holds true for the loops of string theory.
	www.pbs.org /wgbh/nova/elegant/everything.html (1503 words)

	Economist's View: Vibrating Filaments of Imagination
		Whether string theory itself a consistent framework is still an large open question, which is why research is still needed: the original question is still very much open.
		I think what some string theory sceptics are saying is all that fancy math is just a generator that has been adjusted to fit known data, but that doesn't prove a thing by itself.
		As I understand string theory (I have a Ph.D. in experimental particle physics, which is definitely not the same as theoretical, but I have read Dr Greene's book), what it does is give a way to get around the problems of particles being infinitely small and, consequently, infintely dense.
	economistsview.typepad.com /economistsview/2006/10/vibrating_filam.html (6127 words)

	Vibrating string - Definition, explanation
		is the speed of propagation of the wave in the string.
		Once we know the speed of propagation, it is almost immediate to find the frequency of the sound produced by the string.
		is the length of the vibrating part of the string.
	www.calsky.com /lexikon/en/txt/v/vi/vibrating_string.php (229 words)

	Vibrating String
		If the string has a uniform gauge throughout and is kept at a constant tension, then reducing the length by 1/2, for example, will cause the the pitch to double, or increase by an octave.
		Does any of this relate to the fact that if a violin string is vibrating at a certain frequency and then is made half as long by moving the finger half way up the finger board, the frequency of vibration will double sounding a pitch an octave higher than the original.
		Since the model isolates the tiny segment from the rest of the string, then it is the mass of the tiny segment that is used in the frequency calculation, and the rest of the string is just the tensions on the ends of the segment.
	www.physicsforums.com /showthread.php?t=9106 (2323 words)

	The Rockefeller University - String Fever
		You have a string, and the string is vibrating in different modes.
		So, string theory has the potential of unifying quantum mechanics and the theory of general relativity, the world of the small with the world of the large.
		And now Democritus had the atom, Pythagoras said everything is mathematics, but with string theory, you have both: you have the mathematics, and then you have the atom, which is a string, and the different vibrational modes give different particles.
	www.rockefeller.edu /events/string_fever/transcript.php (1169 words)

	Novax Guitars: Information: Technical: Vibrating String
		Intonation is adjusted in the typical way, using the 12th fret harmonic sounding against the string fretted at the 12th fret.
		The saddle for the high E and B string on the guitar (G on bass instruments) may need a longer intonation screw to allow the saddle to move forward farther on the bridge base plate.
		In some cases the spring may need to be removed from the low E string saddle to allow it to move farther back.
	www.novaxguitars.com /neck-installation.html (422 words)

	The Acoustics of Bells
		This movement causes alternate areas of compression and rarefaction in the vibrating medium-a bunching together and spreading apart of the particles-which may be a gas (such as the air), a liquid, or a solid.
		It has been determined that the vibrating segments producing the partials of the minor third and the fifth are separated by six nodal meridians forming three wavelengths; those producing the nominal (octave of the fundamental) are separated by eight meridians forming four wavelengths.
		However, the bell and string differ in one respect: whereas the string's length is equal to half the wavelength of its fundamental, the bell's circumference encompasses two wavelengths of the equivalent frequency.
	www.msu.edu /~carillon/batmbook/chapter5.htm (7709 words)

	Vibrating String Physics
		Each mode of vibration (called a harmonic) is orthogonal, and each is a solution to the equation.
		The general effects of friction on the guitar string are not large.
		Additionally, the friction 'factor' is a function of the frequency of vibration.
	www.ee.washington.edu /research/sahr/pages/physics.html (894 words)

	VI. Notes (played) on the vibrating string
		For the vibrating string, the most common boundary conditions are the zero Dirichlet conditions:
		The coefficients A and B have to be determined from the initial conditions, that is, by the condition of the string at t=0.
		It is precisely as if we imagine the string to be defined on the interval [-1,1], twice as long as the actual interval, but on the nonphysical part from x=-1 to x=0 we pretend that the shape of the string is defined to give us an odd function: f(-x) = -f(x).
	www.mathphysics.com /pde/ch6wr.html (2255 words)

	String Plucker (Site not responding. Last check: )
		This time animation is constructed from the exact Fourier series for an ideal plucked string, vibrating in a plane, with uniform tension and initial triangular profile as set by the user.
		Note that as the string is plucked closer to the ends, the high- frequency content increases, as expected.
		where y is the vertical displacement of the string at x, x is the distance along the string from the left fixed end, L is the length of the string, T is the string tension, rho is the string linear density, xp is the plucked point, and t is the time.
	www.jensign.com /JavaScience/www/plucker.html (418 words)

	Vibrating String Theory -- Magic Twanger
		I have been reading about string theory and how the most elementary particle in the universe is the string -- a one dimensional loop of string that vibrates.
		The vigor with which a string vibrates determines the identity of the larger mass containing the string.
		The vibrational pattern of a string is a manifestation of the energy of the string.
	forums.howwhatwhy.com /showflat.php?Cat=&Board=physics&Number=-340020&fpart=1 (1668 words)

	Standing Waves on a String
		When the wave relationship is applied to a stretched string, it is seen that resonant standing wave modes are produced.
		An ideal vibrating string will vibrate with its fundamental frequency and all harmonics of that frequency.
		That is, its pitch is its resonant frequency, which is determined by the length, mass, and tension of the string.
	hyperphysics.phy-astr.gsu.edu /hbase/waves/string.html (358 words)

	FRETS.COM
		The string is pressed downward until it touches a fret, effectively shortening the vibrating length of the string and producing the different notes.
		The nut holds the strings in position, and usually defines the end of the vibrating length of the strings at the end opposite the bridge.
		On fretted instruments, the saddle is the part of the bridge over which the string passes and which defines the end of the vibrating string.
	www.frets.com /FRETSPages/General/Glossary/glossary.html (1924 words)

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