Transcription of DERIVATION AND ANALYSIS OF SOME WAVE EQUATIONS
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DERIVATION AND ANALYSIS OF SOME WAVE EQUATIONS
Chapter 4. DERIVATION AND ANALYSIS . OF SOME WAVE EQUATIONS . Wave phenomena are ubiquitous in nature. Examples include water waves , sound waves , electro- magnetic waves (radio waves , light, X-rays, gamma rays etc.), the waves that in quantum mechanics are found to be an alternative (and often better) description of particles, etc. Some features are common for most waves , that they in cases of small amplitude can be well approximated by a simple trigonometric wave function (Section ) Other features differ. In some cases, all waves travel with the same speed ( sound waves or light in vacuum) whereas in other cases, the speed depends strongly on the wave length ( water waves or quantum mechanical particle waves ). In most cases, one can start from basic physical principles and from these derive partial differential EQUATIONS (PDEs) that govern the waves .
4.3. WATERWAVES 5 Wavetype Cause Period Velocity Sound Sealife,ships 10 −1−10 5s 1.52km/s Capillaryripples Wind <10−1s 0.2-0.5m/s Gravitywaves Wind 1-25s 2-40m/s Sieches Earthquakes,storms minutestohours standingwaves
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