41. .: LucidQuest :. A Brief History Of Cymatics jules Antoine lissajous (18221880) - jules lissajous, In 1873, jules Antoinelissajous was awarded the Lacaze Prize for his scientific contributions to http://lucidquest.com/resources/learn/cymatics_2.htm

History of Cymatics II : Root 2 Sky Disk Set : .MP3 Samples : Image Gallery : Link Section ... Receive benefits as a LQ member LQ uses combinations of rhythmic, binaural, and algorithmic methods to deliver soundscape experiences which offer an intense and effective entrainment experience.. A Brief History of Cymatics (Pg 2/3 cont.) Jules Antoine Lissajous (1822-1880) - Jules Lissajous, a French physicist and mathematician, investigated the relationships of sound frequencies, waves, and vibrations. In 1850, his doctoral thesis was based on vibrating bars using Chladni's sand patterns and nodal theories. Lissajous began his experiments with sound waves and vibrations by using tuning forks in water and noting the ripple patterns from different applied frequencies. Lissajous also developed a method for visualizing the waveforms created by vibrations. This optical method of capturing vibrations is represented in his well-known Lissajous Figures. These figures were created by reflecting a light beam from mirrors on two tuning forks vibrating at right angles. The images of these light beams as they reflected off the mirrors were captured on a screen. Before the onset of digital technology, Lissajous Figures were used to represent the frequencies of sound waves in radio signals. This was accomplished by observing the pattern a signal of unknown frequency created when it was combined with a signal of known frequency.

42. University Archives :: Exhibits :: A Favorite Abode Of Science :: Lissajous Figu lissajous figures The optical production of the curves was first demonstratedin 1857 by jules Antoine lissajous (18331880). http://archives.scu.edu/exhibits/sci_inst/30.html

University Archives A Favorite Abode of Science Smithsonian - Lissajous figures Acoustic Instrument Aloysius Varsi, S.J. Lissajous figures Two oscillations one along the x axis and the other along the y axis when added result in a two dimensional motion. The path traced is known as Lissajous figures. The optical production of the curves was first demonstrated in 1857 by Jules Antoine Lissajous (1833-1880). The combination of periodic waves moving back and forth with periodic waves moving up and down create the patterns. Image#: Lissajous figures From J. Lissajous, "Etude Optique des Mouvements Vibratoires," Annales de Chimie et de Physique 51 (1857). A Favorite Abode of Science is strictly prohibited. University Archives, Santa Clara University, 500 El Camino Real, Santa Clara, CA 95053-0500 408-554-4117 : FAX 408-554-5179 Orradre Library Webmaster

43. Lissajous Curve julesAntoine lissajous (1822-1880) discovered these elegant curves (in 1857)while doing his sound experiments. But it is said that the American Nathaniel http://www.2dcurves.com/higher/higherli.html

Lissajous curve higher last updated: where b £ p When the constant a is rational, the curve is algebraic and closed. If a is irrational, the curve fills the area [-1,1] x [-1,1]. It is easy to see that the curves for 1/a and a are equal in form. This means that we can confine ourselves to the case a Jules-Antoine Lissajous (1822-1880) discovered these elegant curves (in 1857) while doing his sound experiments. But it is said that the American Nathaniel Bowditch (1773-1838) found the curves already in 1815. After him the curve bears the name of Bowditch curve Another name that I found is the play curve of Alice The curves are constructed as a combination of two perpendicular harmonic oscillations. Patterns occur as a result of differences in frequency ratio (a) and phase (b). At high school we used the oscilloscope to make the curve visible (nowadays a computer would do), by connecting different harmonic signals to the x- and y-axis entrance. The curves have applications in physics, astronomy and other sciences. Each Lissajous curve can be described with an algebraic equation.

44. The Educational Encyclopedia, Electronic Java Applications, Measurement Circuits lissajous en Français. lissajous figures lissajous figures were discovered bythe French physicist jules Antoine lissajous. He would use sounds of different http://users.pandora.be/educypedia/electronics/javameasurement.htm

EDUCYPEDIA The educational encyclopedia Home Electronics General Information technology ... Science Electronics-theory Analog Audio - acoustics Audio - electronics Audio - loudspeakers ... TV-video-CD-DVD Utilities - tools Cables Calculators Circuits Databank - tables ... Sitemap Java applications Active semiconductors Analog Audio Basic cirvuit theory ... Magnetics Measurement Miscellaneous Modulation Motor Passive semiconductors ... Transmission lines Measurement Alimentation réglable en tension et courant en Français Analog meter in order to use a DC-style meter movement, such as the D'Arsonval design pictured in the applet below, the alternating current must be "rectified" into DC Balayage télévision en Français Cathode rays this tutorial demonstrates how the electrons create ionizing effects from residual gas, which results in the visibility of cathode rays Champ magnétique et champ électrique dans un tube cathodique en Français Electroscope Galvanómetro Galvanómetro balístico Kathodenstrahlröhre in German Measuring current with a DMM Measuring voltage with a DMM Mesures de puissance en Français Multimeter Multimeter Stroboscope en Français Thermomètre à diode en Français Thermomètre à résistance de platine en Français Universeel meter in Dutch Wet van Ohm in Dutch Superheterodyne spectrum analyzer a spectrum analyzer is an extremely useful measurement tool that can show, in the frequency domain, information not readily recognizable with a time domain instrument such as an oscilloscope. For example, the frequency content of a signal (e.g. a fundamental sinusoid and one or more harmonic components) is readily identified with a spectrum analyzer

45. Cymatics - The Science Of The Future? right) This after the French mathematician julesAntoine lissajous, who, These lissajous figures are all visual examples of waves that meet each http://www.mysticalsun.com/cymatics/cymatics.html

Is there a connection between sound, vibrations and physical reality? Do sound and vibrations have the potential to create? In this article we will see what various researchers in this field, which has been given the name of Cymatics, have concluded. By Peter Pettersson, translation Yarrow Cleaves n 1787, the jurist, musician and physicist Ernst Chladni published or Discoveries Concerning the Theory of Music. With the help of a violin bow which he drew perpendicularly across the edge of flat plates covered with sand, he produced those patterns and shapes which today go by the term Chladni figures. (se left) What was the significance of this discovery? Chladni demonstrated once and for all that sound actually does affect physical matter and that it has the quality of creating geometric patterns. Lissajous Figures In 1815 the American mathematician Nathaniel Bowditch began studying the patterns created by the intersection of two sine curves whose axes are perpendicular to each other, sometimes called Bowditch curves but more often Lissajous figures.

46. Lissajous Biography of jules lissajous (18221880) jules lissajous entered Ecole NormaleSupérieure in 1841. Afterwards he became professor of mathematics at the http://www.nmhs.nusd.k12.ca.us/Nmhs/Departmentwebsites/Math/Lissajous.htm

Jules Antoine Lissajous Born: 4 March 1822 in Versailles, France Died: 24 June 1880 in Plombières, France Jules Lissajous entered Ecole Normale Supérieure in 1841. Afterwards he became professor of mathematics at the Lycée Saint-Louis. In 1850 he was awarded a doctorate for a thesis on vibrating bars using Chladni's sand pattern method to determine nodal positions. In 1874 Lissajous became rector of the Academy at Chambéry, then in 1875 he was appointed rector of the Academy at Besançon. Lissajous was interested in waves and developed an optical method for studying vibrations. At first he studied waves produced by a tuning fork in contact with water. In 1855 he described a way of studying acoustic vibrations by reflecting a light beam from a mirror attached to a vibrating object onto a screen. Duhamel had tried to demonstrate these vibrations with a mechanical linkage but Lissajous wanted to avoid the problems caused by the linkage. He obtained Lissajous figures by successively reflecting light from mirrors on two tuning forks vibrating at right angles. The curves are only seen because of persistence of vision in the human eye. Lissajous studied beats seen when his tuning forks had slightly different frequencies, in this case a rotating

47. Lissajous Curve - Wikipedia, The Free Encyclopedia In mathematics, a lissajous curve (lissajous figure or Bowditch curve) is thegraph of the system and later in more detail by jules Antoine lissajous. http://en.wikipedia.org/wiki/Lissajous_curve

Wikimedia needs your help in its 21-day fund drive. See our fundraising page Over US$220,000 has been donated since the drive began on 19 August. Thank you for your generosity! Lissajous curve From Wikipedia, the free encyclopedia. Lissajous figure on an Oscilloscope Lissajous figure in three dimensions In mathematics , a Lissajous curve Lissajous figure or Bowditch curve ) is the graph of the system of parametric equations which describes complex harmonic motion . This family of curves was investigated by Nathaniel Bowditch in , and later in more detail by Jules Antoine Lissajous The appearance of the figure is highly sensitive to the ratio a b . For a ratio of 1, the figure is an ellipse , with special cases including circles A B radians ) and lines (δ = 0). Another simple Lissajous figure is the parabola a b = 2, δ = π/2). Other ratios produce more complicated curves, which are closed only if a b is rational . The visual form of these curves is often suggestive of a three-dimensional knot , and indeed the many kinds of knots, including those known as Lissajous knots , project to the plane as Lissajous figures.

48. Lissajous Figures lissajous Figures were first described in 1815 by Nathaniel Bowditch (17731838), was first demonstrated in 1857 by jules Antoine lissajous (1833-1880), http://physics.kenyon.edu/EarlyApparatus/Oscillations_and_Waves/Lissajous_Figure

Lissajous Figures Lissajous Figures were first described in 1815 by Nathaniel Bowditch (1773-1838), who is best known today for his book, "The New American Practical Navigator", still available today. He also wrote widely on mathematics and astronomy, while pursuing a career as a navigator, surveyor, actuary and insurance company president, as well as being a member of the Corporation of Harvard College. The optical production of the curves was first demonstrated in 1857 by Jules Antoine Lissajous (1833-1880), using apparatus similar to that at the left. Today we can do the same experiment more easily with a laser beam that reflects from the two mirrors vibrating at right angles to each other and then traces the Lissajous figure on the wall. On the left is a pair of tuning forks permanently mounted at right angles to each other. The apparatus is shown in the 1900 catalogue of Max Kohl at a price of 66 Marks. It is in the collection at St. Mary's College in Notre Dame Indiana. The frequency of the tuning forks in both sets of apparatus can be varied by sliding masses up and down.

49. The Structure And Dynamics Of Waves And Vibrations By Hans Jenny right) This after the French mathematician julesAntoine lissajous, who, In fact, one can produce lissajous figures even if the frequencies are not http://www.world-mysteries.com/sci_cymatics.htm

World-Mysteries.com presents Cymatics - The Science of the Future? Is there a connection between sound, vibrations and physical reality? Do sound and vibrations have the potential to create? In this article we will see what various researchers in this field, which has been given the name of Cymatics, have concluded. By Peter Pettersson, translation Yarrow Cleaves In 1787, the jurist, musician and physicist Ernst Chladni published Entdeckungen über die Theorie des Klangesor Discoveries Concerning the Theory of Music.In this and other pioneering works, Chladni, who was born in 1756, the same year as Mozart, and died in 1829, the same year as Beethoven, laid the foundations for that discipline within physics that came to be called acoustics, the science of sound. Among Chladni´s successes was finding a way to make visible what sound waves generate. With the help of a violin bow which he drew perpendicularly across the edge of flat plates covered with sand, he produced those patterns and shapes which today go by the term Chladni figures. (se left) What was the significance of this discovery? Chladni demonstrated once and for all that sound actually does affect physical matter and that it has the quality of creating geometric patterns. Chladni figures.

50. Oscilloscope Tutorials. called a lissajous pattern (named for French physicist jules Antoine lissajousand From the shape of the lissajous pattern, you can tell the phase http://oscilloscope-tutorials.com/Oscilloscope\PhaseShift.asp

All about Oscilloscopes The Oscilloscope Oscilloscope Terminology Setting Up ... Measurement Techniques Phase Shift Measurements The horizontal control section may have an XY mode that lets you display an input signal rather than the time base on the horizontal axis. (On some digital oscilloscopes this is a display mode setting.) This mode of operation opens up a whole new area of phase shift measurement techniques. The phase of a wave is the amount of time that passes from the beginning of a cycle to the beginning of the next cycle, measured in degrees. Phase shift describes the difference in timing between two otherwise identical periodic signals. One method for measuring phase shift is to use XY mode. This involves inputting one signal into the vertical system as usual and then another signal into the horizontal system. (This method only works if both signals are sine waves.) This set up is called an XY measurement because both the X and Y axis are tracing voltages. The waveform resulting from this arrangement is called a Lissajous pattern (named for French physicist Jules Antoine Lissajous and pronounced LEE-sa-zhoo). From the shape of the Lissajous pattern, you can tell the phase difference between the two signals. You can also tell their frequency ratio. Figure 6 shows Lissajous patterns for various frequency ratios and phase shifts. Figure 6: Lissajous Patterns Interesting Links Test Equipment Catalog1 Test Equipment Catalog2 Learn all about spectrum analyzes Browse thousands of

51. Cymatics History jules lissajous, a French physicist and mathematician, investigated the In 1873, jules Antoine lissajous was awarded the Lacaze Prize for his scientific http://www.spiritofmaat.com/archive/oct3/history.htm

Spirit of Ma'at: A Brief History of Cymatics Ernst Florenz Friedrich Chladni (1756-1827) In 1786, he Chladni was able to identify the quantitative relationships governing the transmission of sound, using mathematical analysis to interpret his findings. As the first person to mathematically quantify the relationships governing sound transmission, he came to be known as the Father of Acoustics. Chladni's experiments consisted of using geometrically shaped, thin glass or metal plates covered with fine sand sprinkled uniformly over the surfaces. He utilized a violin bow to strum along the edge of these plates. The resulting sand patterns illustrated the effects of the vibrations of the violin frequencies. The sand, under the influence of the vibrations of these sound frequencies, moved from the antinodes, collecting symmetrically in nodal lines, forming intricate patterns. Chladni proved that the pressure derived from sound waves affects physical matter. His documentation was so detailed that, following his methods, the effects of his experiments are reproducible even today. His diagrams depicting the sound patterns derived from these experiments have come to be called Chladni Figures. Chladni also studied the pitch of sound by measuring the changes in frequency that occur in a gas-filled cylinder. Using an organ pipe filled with gas, he was able to show that the pitch of sound is dependent upon the molecular structure of the gas through which it propagates.

52. Lissajous Curves@Everything2.com lissajous curves or lissajous figures are sometimes called Bowditch They werestudied in more detail (independently) by julesAntoine lissajous in 1857. http://www.everything2.com/?node_id=1277127

53. MIT Lincoln Laboratory - MIT Lincoln Laboratory Logo named for the French mathematician julesAntoine lissajous, are also known Overhage drew a lissajous figure based on the superposition of two simple http://www.ll.mit.edu/about/lissajous.html

Lincoln Laboratory Logo The Lissajous figures , named for the French mathematician Jules-Antoine Lissajous , are also known as Bowditch curves after their discoverer, Nathaniel Bowditch , the mathematician from Salem, Massachusetts. The history that follows is taken from MIT Lincoln Laboratory: Technology in the National Interest , ed. Eva C. Freeman. Lexington, Mass.: MIT Lincoln Laboratory, 1995. The MIT Lincoln Laboratory Logo, which first appeared in February 1958 in the Lincoln Laboratory Bulletin, was conceived by Carl Overhage, the Laboratory's fourth director. Overhage drew a Lissajous figure based on the superposition of two simple harmonic vibrations and commissioned retired Brigader General Robert Steinle and the firm Advertising Designers of Los Angeles to transform the Lissajous figure into an artistic image. The two L's rotated 180 degrees with respect to each other stand for Lincoln Laboratory. They form a rectangle enclosing the Lissajous figure generated by the parametric equations x = 3 sin(8 pi t/T) and y = 4 sin(6 pi t/T). The figure is traced along the horizontal axis x and the vertical axis y as the variable t progresses from t = to T.

54. Lissajous Or Bowditch Curves - National Curve Bank The National Curve Bank Project for Students of Mathematics lissajous or Bowditch now usually named for the French physicist, julesAntoine lissajous. http://curvebank.calstatela.edu/lissajous/lissajous.htm

Back to . . . Curve Bank Home Classics Index Page Lissajous or Bowditch Curves Parametric Equations Note: The n determines the number of complete loops. The Slide Show on the right illustrates different values for the constant terms. Replay the animation Replay the Slide Show MATHEMATICA Code Also, these curves are easily entered and modified on a graphing calculator. American Nathaniel Bowditch "I never come across one of Laplace's 'Thus it plainly appears' without feeling sure that I have hours of hard work before me to fill up the chasm and find out and show how it plainly appears." Nathaniel Bowditch Historical Sketch Nathaniel Bowditch (1773 - 1838) was the first American to receive international recognition as a mathematician. Moreover, he was the first to investigate a family of curves now usually named for the French physicist, Jules-Antoine Lissajous. Lissajous independently published his work much later in 1857. Bowditch, working in the isolation of New England's Salem and Boston areas, held a life-long fascination with doing tedious calculations. He learned Latin and several other languages in order to read the mathematical publications being imported from Europe. In particular, he is known to have studied Newton's

55. Lissajous Figures Most often, the pattern was a lissajous Figure. jules Antoine lissajous (18221880)was a French physicist who was interested in waves, and around 1855 http://www.jmargolin.com/mtest/LJfigs.htm

Lissajous Figures by Jed Margolin In the old days, whenever they showed an engineer working, there was usually an oscilloscope nearby with a pattern on the screen. Most often, the pattern was a Lissajous Figure. Jules Antoine Lissajous (1822-1880) was a French physicist who was interested in waves, and around 1855 developed a method for displaying them optically by reflecting a light beam from a mirror attached to a vibrating object such as a tuning fork. You might wonder why he didn't just use an oscilloscope. It was probably because the Cathode Ray Tube hadn't been invented yet. (It was invented in 1897 by Karl Ferdinand Braun). A Lissajous figure is produced by taking two sine waves and displaying them at right angles to each other. This is easily done on an oscilloscope in XY mode. In the following examples the two sine waves have equal amplitudes. When the two sine waves are of equal frequency and in-phase, you get a diagonal line to the right . When the two sine waves are of equal frequency and 180 degrees out-of-phase you get a diagonal line to the left. When the two sine waves are of equal frequency and 90 degrees out-of-phase you get a circle.

56. Tobias Preußer - Lissajous Figuren Translate this page senkrecht stehenden Ebenen schwingen kann, beobachtet man lissajous-Figuren,die zuerst von jules Antoine lissajous 1857 in Paris demonstriert wurden http://cips02.physik.uni-bonn.de/~preusser/applets/lissajous/lissajous.html

Lissajous Figuren Bei einem System, das gleichzeitig in zwei aufeinander senkrecht stehenden Ebenen schwingen kann, beobachtet man Lissajous-Figuren, die zuerst von Jules Antoine Lissajous 1857 in Paris demonstriert wurden: Ihr Browser kann leider keine Java-Applets anzeigen. Schade. f (t) = A sin (w t) f (t) = A sin (w t + p) Im Fall der oben zu sehenden Figuren ist die Frequenz w ganzzahliges Vielfaches der Frequenz w erfolgt alle paar Minuten neu. Die beiden maximalen Amplituden sind im Applet immer gleich. Die Phase p Suchen Sie sich einen Punkt der Figur. Wenn die erste Schwingung nun die Amplitude hat, die Sie in diesem Punkt auf der X-Achse ablesen, dann hat die zweite Schwingung die Amplitude, die Sie in diesem Punkt auf der Y-Achse ablesen. p p Document changed last on (preusser@cips02.physik.uni-bonn.de) 1996 Access statistics by Nedstat

57. Tobias Preußer - Java-Applets Translate this page Dieses Applet zeigt sogenannte lissajous - Figuren, die in der Physik auftreten, Sie wurden zuerst von jules Antoine lissajous in Paris 1857 beobachtet. http://cips02.physik.uni-bonn.de/~preusser/applets/applets.html

Java-Applets Lissajous-Figuren Dieses Applet zeigt sogenannte Lissajous - Figuren Minesweeper Building Blocks Tetris® is a trademark of "The Tetris Company". Stadtplan zur Homepage. Document last modified on (preusser@cips02.physik.uni-bonn.de) 1996 Acess statistics by Nedstat

58. Encyclogram [encyclopedia] Encyclogram draws harmonographs, spirographs, and lissajous figures. was pioneered by the French physicist, jules Antoine lissajous in 1857. http://kosmoi.com/Science/Mathematics/Graphs/Encyclo/more.shtml

EncycloZine Astronomy Biology Chemistry ... Calculus With Analytic Geometry Ron Larson, Robert P. Hostetler, Bruce H. Edwards Geometry Larson Michael Sullivan Discovering Geometry: An Inductive Approach Michael Serra Geometry Ray Jurgensen, Richard G. Brown College Algebra with Modeling and Visualization (3... Gary K. Rockswold Richard Rhoad, George Milauskas, Robert Whipple Calculus With Analytic Geometry, Seventh Edition Ron Larson The Misbehavior of Markets Benoit Mandelbrot, Richard L. Hudson Geometry of Design: Studies in Proportion and Comp... Kimberly Elam Encyclogram Kosmoi.com Science Mathematics Graphs ... Pictures by AR Harmonographs, Spirographs, and Lissajous Figures Encyclogram draws harmonographs, spirographs , and Lissajous figures . The decaying motion of the plot fills in the shapes with their spiralling-in echo. Encyclogram can also draw the curves in varying colors against a black background, resulting in breath-taking works of art that can be as beautiful as fractals . See the gallery of examples Harmonographs are mathematically the sums of several harmonic motions in the x and y directions, decayed over time. If the decay is removed, and there are only two harmonic motions (sinusoids), one in x and one in y, then the graphs are

59. Lissajous Figures Named after the French mathematician julesAntoine lissajous. lissajous figurescan be thought of as a simple physical system with springs. http://www.physics.emory.edu/~weeks/ideas/lissajou.html

Eric Weeks - personal pages - misc Lissajous Figures weeks@physics.emory.edu This was created with the following command: I don't know much about Lissajous figures; probably there's some place else on the web that you could learn a whole lot about them from . Basically they're sort of failed circles, or rather, a circle is the simplest Lissajous figure. By varying the rate at which X and Y change (changing the 18 and 20 above) you change how the Lissajous figure forms. Named after the French mathematician Jules-Antoine Lissajous. Lissajous figures can be thought of as a simple physical system with springs. Suppose you have a weight hanging from a spring, and you pull the weight downward and let go. If you graph the vertical position -vs- time, you get a sine wave. (A real spring would also have friction, so the sine wave would get smaller as the spring lost energy.) Imagine you have a weight hanging from a spring, with two horizontal springs attached to it, making an upside down T with the horizontal springs attached to walls. The weight can now move from side to side as well; if you pull it to one side, and let go, the weight will move in a sine wave again except with the horizontal position being what oscillates. If you have both horizontal and vertical springs, and you move the weight diagonally (so that all of the springs are stretched) and let go, the position of the weight will trace out a Lissajous figure. The frequencies of the springs will determine how the Lissajous figure looks. For example, the figure at the top of the page might be from a weight/spring system with a vertical frequency of 1/20 and a horizontal frequency of 1/18.

60. Joost Rekveld | Symmetry And Harmonics and physicist jules lissajous, later in the nineteenth century. lissajouspatterns have found many applications in the twentieth century. http://www.lumen.nu/rekveld/texts/symhar.html

symmetry and harmonics Joost Rekveld, Rotterdam, 24-11-1998 figure 1: mirror cabinet of Z.Traber, 1675 harmonic images Pure intervals are pure for a physical reason: if the ratio of frequencies of two soundwaves can be described in small numbers, the minima and maxima of these waves overlap nicely. This makes a chord sound at rest. If the ratio of frequencies is more complex, these overlaps form a more complex pattern and the tones do not blend properly or a difference tone appears. Similar phenomena occur if images are generated using vibrations. Several physicists from the 19th century did experiments in this direction. Ernst Chladni wrote his book 'Entdeckungen im Reich des Klanges' in 1787. It is the first general treatise on acoustics. He illustrated it with diagrams of the vibrations of thin metal plates (fig. 2). For these experiments he covered the plates with a thin layer of sand and made them vibrate by striking them with a bow. The vibrations displaced the sand toward the locations on the plate where the waves in the metal formed 'knots'. Chladni analized these sandpatterns, classified them according to shape and tried to understand the relationship with their corresponding pitch. He concluded that a vibrating plate generates a set of tones (fundamental and harmonics) that corresponds with the harmonic series produced by a vibrating string. figure 2: sound figures by Chladni, 1787

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