History of Chladni's Law
f ~ (m+2n)^2
The story behind the equation:
Ernest Florens Friedrich Chladni of Saxony is often respectfully referred to as "the Father of Acoustics". Indeed, his body of work on the vibration of plates has served as the foundation of many experiments by countless other scientists, including Faraday, Strehlke, Savart, Young, and especially Mary Desiree Waller. Chladni's study consisted of vibrating a fixed, circular plate with a violin bow and then sprinkling fine sand across it to show the various nodal lines and patterns. The experiment is particularly rewarding in that high frequencies often exhibit strikingly complex patterns (see the pictures on the
image page). In fact, Chladni's demonstrations in many royal academies and scientific institutions frequently drew large crowds who were duly impressed with the aesthetically sophisticated qualities of vibrating plates. Napoleon himself was so pleased with Chladni's work that he commissioned the further study of the mathematical principles of vibrating plates which then spurred a plethora of research in waves and acoustics. While experimental methods and equipment have been much improved in the last 200 years, Chladni's law and original patterns are still regularly employed to study plate vibrations.
References:
Rossing, Thomas D. "Chladni's Law for Vibrating Plates."
American Journal of Physics.Vol 50. no 3. March, 1982.
