Write two uses of lissajous figure
Answers
Jules Lissajous entered the École Normale Supérieure in 1841. In 1847 he became professor of mathematics at the Lycée Saint-Louis, holding this position until 1874. He was awarded a doctorate in 1850 for a thesis on vibrating bars using Chladni's sand pattern method to determine nodal positions.
Lissajous was interested in waves and developed an optical method for studying vibrations. He wanted to be able to see the waves that were created by vibrations, usually expressed in the form of sound. At first he studied waves produced by a tuning fork in contact with water, studying the ripples that were caused. Working on these ideas, he published Sur la position des noeuds dans les lames qui vibrent transversalement (1850). 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. He published Sur un cas particulier de stéréoscopie fourni par l'étude optique des mouvements vibratoires (1856), then his major work Mémoire sur l'étude optique des mouvements vibratoires
Jean-Marie 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 ellipse is seen.
Lissajous was praised by his contemporaries for his work and awarded the Lacaze Prize in 1873 for his optical observation of vibration and, in particular, "for his beautiful experiments". Perhaps it is entirely fair that "his beautiful experiments" were a major factor in the award of the prize since Lissajous figures had been investigated forty years earlier by Nathaniel Bowditch. He had produced them in 1815 with a compound pendulum and, because of this, sometimes the figures are referred to as Bowditch figures or Lissajous-Bowditch figures. We should note, however, that Lissajous' work was entirely independent of that of Bowditch.
Today Lissajous figures became a standard topic in physics texts and demonstrations. The experiments were exhibited at the Paris Universal Exhibition in 1867. We have noted above John Tyndall's discussion of Lissajous's experiments, and he described them in detail in his acoustics text. Lord Rayleigh also discussed Lissajous figures in his classical treatise on acoustics. Hermann von Helmholtz used Lissajous' instruments in his study of string vibrations.
In 2016 the Exploratory Record Label - Audiobulb Records made a Lissajous software application to use with music.
INFORMATION PAGE: software module & M4L
Lissajous is a real-time audio reactive graphics application (available for MaxForLive) and inspired by the work of Jules Antoine Lissajous.
The media project is born with the purpose of investigating the relationship between sound and vision, chaos and order, closely related to astronomy, mathematics & physics. It explores the field of harmony and disorder and let the user dip into an elegant, dreamlike, minimalistic yet chaotic space which reflects the complex rules of the universe in all its abstract beauty.
The software shows sound oscillations as XY matrix functions and creates complex graphics curves. Lissajous graphically describes sound and allow observation of constantly varying signal voltage of two audio signals as function of time. Video generated by sound can be controlled in endless ways by giving to the user the possibility of a whole-new range of interactions.