Velocity, wavelength, freq. relationship

[FrankMak]

The relationship between velocity, wavelength and frequency is expressed by the equation, velocity = wavelength x frequency. I know when Thomas Young used this relationship for light waves, but I cannot find any reference when this relationship was first presented for other than electromagnetic waves.

When and who first identified this relationship?

 

[Astronuc]

The idea of a group velocity distinct from a wave's phase velocity was first proposed by William Rowan Hamilton in 1839, and the first full treatment was by Rayleigh in his "Theory of Sound" in 1877.

http://en.wikipedia.org/wiki/Group_velocity
http://en.wikipedia.org/wiki/Phase_velocity

http://en.wikipedia.org/wiki/William_Rowan_Hamilton
http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Hamilton.html

However, in 1670, Christiaan Huygens became the first person to explain how wave theory can also account for the laws of geometric optics. By 1678, Hygyens had developed a theory of light as "longitudinal pulses" similar to sound.

http://www.tiscali.co.uk/reference/encyclopaedia/hutchinson/m0016131.html
http://en.wikipedia.org/wiki/Christiaan_Huygens

After early work by Newton, the eighteenth and early nineteenth century French mathematicians Laplace, Lagrange, Poisson, and Cauchy made real theoretical advances in the linear theory of water waves; in Germany, Gerstner considered nonlinear waves, and the brothers Weber performed fine experiments. Later in Britain during 1837–1847, Russell, Green, Kelland, Airy, and Earnshaw all made substantial contributions, setting the scene for subsequent work by Stokes and others.

http://arjournals.annualreviews.org/doi/abs/10.1146/annurev.fluid.36.050802.122118?tokenDomain=eprints&tokenAccess=ntKxUcsyXeywpgFQRASc&forwardService=showFullText&cookieSet=1&journalCode=fluid

George Stokes made contributions to wave theory - but in the 1800's.
http://www-history.mcs.st-andrews.ac.uk/Biographies/Stokes.html
http://en.wikipedia.org/wiki/George_Gabriel_Stokes

But Vitruvius may have determined wave velocity - Vitruvius and the Early History of Wave Theory
http://links.jstor.org/sici?sici=0040-165X(196322)4%3A3%3C282%3AVATEHO%3E2.0.CO%3B2-6
(I couldn't find an explicit statement that he did).

The mathematical theory of sound propagation began with Isaac Newton (1642-1727), whose Principia (1686) included a mechanical interpretation of sound as being "pressure" pulses transmitted through neighboring fluid particles.

I think the measurement of speed requires an accurate measurement of time, specifically short increments, like seconds. One would have to determine when time was measured in short increments, which enabled the measurement of the speed of propagation. Prior to that, wavelength was probably understood, but not wave velocity.

The Wave Theory of Sound > A Little History
http://www.cartage.org.lb/en/themes/sciences/physics/Acoustics/history/TheorySound/Littlehistory.htm
which is also supported here
http://asa.aip.org/pierce.html

I bet James Burke has written something about this in his Connections essays.
http://en.wikipedia.org/wiki/Connections_(TV_series)

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This is kind of neat! http://www.walter-fendt.de/ph14e/huygenspr.htm

 

[FrankMak]

Astronuc, thanks for your research. It is conceiveable that the knowledge of the relationship between velocity, wavelength and frequency may have been known over 2,000 years ago or before, but unless an ancient document is identified containing this material we will not know for sure.

The material in the URL discusses mathematical history and strongly suggests some of the "new" mathematics are probably "rediscoveries".

http://graham.main.nc.us/~bhammel/MATH/cgpredux.html