6B Ch 15 (Official)

The elements the total kinetic energy in one

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Unformatted text preview: ifferential equation: dK =1/2 ( x) vy2 = 1/2 2A2cos2(kx – t) dx Energy in a string • Integrating over all the elements, the total kinetic energy in one wavelength is K = 1/4 2A 2 • The total potential energy in one wavelength is (K=U for each element of the wave, remember the harmonic oscillator!)) U = 1/4 2A 2 • This gives a total energy of E = K + U = 1/2 2A 2 1/2m 2A 2=2 2mf2A 2 Power Associated with a Wave in a String • The power is the rate at which the energy is being transferred: • The power transfer by a sinusoidal wave on a string is proportional to the – Square of the frequency – Square of the amplitude – Speed of the wave E = K + U = 1/2m 2A 2=2 2mf2A2 E = K + U =2 2mf2A2= P=E/t Svf Svtf Linear Wave Equation, General • The equation can be written as • This applies in general to various types of traveling waves – y represents various positions • For a string, it is the vertical displacement of the elements of the string • For a sound wave, it is the longitudinal position of the elements from the equilibrium position The Principle of Superposition Superposition:...
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This document was uploaded on 02/21/2014 for the course CHEM 110A 110a at UCLA.

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