Faraday wave

Faraday waves observed in water in a Petri dish, vibrated at a frequency of about 50 hertz.
Faraday waves in a singing bowl

Faraday waves, also known as Faraday ripples, named after Michael Faraday (1791–1867), are nonlinear standing waves that appear on liquids enclosed by a vibrating receptacle. When the vibration frequency exceeds a critical value, the flat hydrostatic surface becomes unstable. This is known as the Faraday instability. Faraday first described them in an appendix to an article in the Philosophical Transactions of the Royal Society of London in 1831.[1][2]

If a layer of liquid is placed on top of a vertically oscillating piston, a pattern of standing waves appears which oscillates at half the driving frequency, given certain criteria of instability.[3] This relates to the problem of parametric resonance. The waves can take the form of stripes, close-packed hexagons, or even squares or quasiperiodic patterns. Faraday waves are commonly observed as fine stripes on the surface of wine in a wine glass that is ringing like a bell. Faraday waves also explain the 'fountain' phenomenon on a singing bowl.

The Faraday wave and its wavelength is analogous to the de Broglie wave with the de Broglie wavelength in de Broglie–Bohm theory in the field of quantum mechanics.[4]

  1. ^ Faraday, M. (1831) "On a peculiar class of acoustical figures; and on certain forms assumed by a group of particles upon vibrating elastic surfaces", Philosophical Transactions of the Royal Society (London), vol. 121, pp. 299–318. "Faraday waves" are discussed in an appendix to the article, "On the forms and states assumed by fluids in contact with vibrating elastic surfaces". This entire article is also available on-line (albeit without illustrations) at "Electronic Library".
  2. ^ Others who investigated "Faraday waves" include: (1) Ludwig Matthiessen (1868) "Akustische Versuche, die kleinsten Transversalwellen der Flüssigkeiten betreffend" (Acoustic experiments concerning the smallest transverse waves of liquids), Annalen der Physik, vol. 134, pp. 107–17; (2) Ludwig Matthiessen (1870) "Über die Transversalschwingungen tönender tropfbarer und elastischer Flüssigkeiten" (On the transverse vibrations of ringing low-viscosity and elastic liquids), Annalen der Physik, vol. 141, pp. 375–93; (3) John William Strutt (Lord Rayleigh) (1883), "On the crispations of fluid resting upon a vibrating support," Philosophical Magazine, vol. 16, pp. 50–58; (4) Thomas Brooke Benjamin and Fritz Joseph Ursell (1954), [1]"The stability of the plane free surface of a liquid in vertical periodic motion" Proceedings of the Royal Society A, vol. 225, issue 1163.
  3. ^ Wright, P.H.; Saylor, J.R. (September 2003). "Patterning of particulate films using Faraday waves" (PDF). Review of Scientific Instruments. 74 (9): 4063–70. Bibcode:2003RScI...74.4063W. doi:10.1063/1.1602936. Retrieved 4 May 2016.
  4. ^ "John W. M. Bush: Quantum mechanics writ large" (PDF). Archived from the original (PDF) on 15 December 2017. Retrieved 21 October 2010.