Identifier: studyofpropagati00shew (find matches)
Title: A study of the propagation, refraction, reflection, interference and diffraction of ripple waves
Year: 1914 (1910s)
Authors: Shewhart, Walter Andrew
Subjects: Waves Hydrodynamics Theses
Publisher:
Contributing Library: University of Illinois Urbana-Champaign
Digitizing Sponsor: University of Illinois Urbana-Champaign

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+ SttT (J7) 2?T pt\ if only those vibrations are considered which have infinitely smallvibrations so that tanh kl = 1. j. For any liquid of given surface tension T it is seen from equa-tion (1.7) that the velocity becomes the equal to the square root ofthe sum of two functions of the wave length, which themselves are con-stants, or we may write V = Vf,(/0 + e,(Al .The velocity will therefore have a minimum --alue when the sumf, (X) + Q,()\) is a minimum or as can be shown by calculus or algebrawhen f,.(^) = A,(/\). Substituting the values in these functions and solving for the wave length it is fpund that A = 27rvZL & corresponds to the minimum value of V, and using this value to obtainthe velocity we have V = V2 (f-f For water, where T = 75 dynes the value of the minimum velocityis 23 cm/sec. and corresponds to a wave length A = 1.7 cm. The bestidea of the relation of wave length to velocity can perhaps be gained 21 Poynting and Thomson, Properties of l.iatterw 5 Ed., page .158.
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♦ t 11 from the curve shown on opposite page. Lord Kelvin has defined a ripple aa the wave whose length isleas than the wave length for which we obtain a minimum velocity andincludes the dotted area under the curve, whereaa he has defined acapillary ripple aa one whoae length is so small as to render negli-gible the first term (g M in the value of the velocity squared. air III SUMMARY Thus it has been shown that if the fluid ia practically non-compressible, and nonviscous so that the forces remain conservative,and if the vibrations of the liquid have infinitesimal magnitudes,and if the motion is irrotational then the surface disturbance isrepresentable to a close approximation by a sine curve. Therefore,if the above conditions are satisfied it i3 evident that ripple wavesmay be studied as examples of general wave motion. The experimentalwork in Part II has been built up on the basis of this conclusion. 22 Watsons Text Book of Physics. PART II EXPERIMENTAL j nnT^ *v THIS INVESTIGATIO

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