Linear and nonlinear waves
TLDR
The study of waves can be traced back to antiquity where philosophers, such as Pythagoras, studied the relation of pitch and length of string in musical instruments and the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt in his treatise Theory of Sound.Abstract:
The study of waves can be traced back to antiquity where philosophers, such as Pythagoras (c.560-480 BC), studied the relation of pitch and length of string in musical instruments. However, it was not until the work of Giovani Benedetti (1530-90), Isaac Beeckman (1588-1637) and Galileo (1564-1642) that the relationship between pitch and frequency was discovered. This started the science of acoustics, a term coined by Joseph Sauveur (1653-1716) who showed that strings can vibrate simultaneously at a fundamental frequency and at integral multiples that he called harmonics. Isaac Newton (1642-1727) was the first to calculate the speed of sound in his Principia. However, he assumed isothermal conditions so his value was too low compared with measured values. This discrepancy was resolved by Laplace (1749-1827) when he included adiabatic heating and cooling effects. The first analytical solution for a vibrating string was given by Brook Taylor (1685-1731). After this, advances were made by Daniel Bernoulli (1700-82), Leonard Euler (1707-83) and Jean d’Alembert (1717-83) who found the first solution to the linear wave equation, see section (3.2). Whilst others had shown that a wave can be represented as a sum of simple harmonic oscillations, it was Joseph Fourier (1768-1830) who conjectured that arbitrary functions can be represented by the superposition of an infinite sum of sines and cosines now known as the Fourier series. However, whilst his conjecture was controversial and not widely accepted at the time, Dirichlet subsequently provided a proof, in 1828, that all functions satisfying Dirichlet’s conditions (i.e. non-pathological piecewise continuous) could be represented by a convergent Fourier series. Finally, the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt (Lord Rayleigh, 1832-1901) in his treatise Theory of Sound. The science of modern acoustics has now moved into such diverse areas as sonar, auditoria, electronic amplifiers, etc.read more
Citations
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Journal ArticleDOI
Hitchhiker's guide to the fractional Sobolev spaces
TL;DR: In this article, the authors deal with the fractional Sobolev spaces W s;p and analyze the relations among some of their possible denitions and their role in the trace theory.
Journal ArticleDOI
Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).
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The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations
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Discrete breathers — Advances in theory and applications
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Introduction to Physical Oceanography
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References
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Book
Nonlinear Waves, Solitons and Chaos
Eryk Infeld,George Rowlands +1 more
TL;DR: The second edition of as mentioned in this paper is the only text at this level to embrace a universal approach to three major developments in classical physics; namely nonlinear waves, solitons and chaos.
Book
Initial-boundary value problems and the Navier-Stokes equations
Heinz-Otto Kreiss,Jens Lorenz +1 more
TL;DR: The Navier-Stokes equations under initial and boundary conditions were studied in this paper, where they were shown to be incompressible in the spatially periodic case and in the constant-coefficient case.
Journal ArticleDOI
The Formation of a Blast Wave by a Very Intense Explosion. II. The Atomic Explosion of 1945
TL;DR: In this article, the authors measured the radius of the luminous globe or "ball of fire" which spread out from the centre of the first atomic explosion in New Mexico, and the radius, R, was determined for a large range of values of t, the time measured from the start of the explosion.
Book
Numerical Computation of Internal and External Flows, Volume 2: Computational Methods for Inviscid and Viscous Flows
TL;DR: In this paper, numerique and ecoulement are used for CFD reference records. But the reference record was created on 2005-11-18, modified on 2016-08-08.