A tension wave along a long cable satisfies

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Oscillations, Waves & Acoustics · Wave motion, the wave equation and wave energy

Conditions of Validity, Ch The three equations, their characteristics and what makes a problem well posed

Problem

A tension wave along a long cable satisfies utt−4uxx=0u_{tt} - 4u_{xx} = 0, with xx in metres and tt in seconds. ((a)) Identify the wave speed cc and write down the two families of characteristics. ((b)) Find the domain of dependence of the point x=5.0 mx=5.0\,\mathrm{m} at t=3.0 st=3.0\,\mathrm{s}.

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