This preview shows page 1. Sign up to view the full content.
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:...
View
Full
Document
This document was uploaded on 02/21/2014 for the course CHEM 110A 110a at UCLA.
 Winter '13

Click to edit the document details