1 General solution to wave equation

General solution TO WAVE EQUATION1I-campus projectSchool-wide Program on Fluid MechanicsModules on waves TWOONE-DIMENSIONAL PROPAGATIONS ince the equation 2 t2=c2 2 governs so many physical phenomena in nature and technology, its properties are basicto the understanding of wave propagation. This chapter is devoted to its analysis whenthe extent of the medium is infinite and the motion is one dimensional. To be bespecific, physical discussions are made for shallow-water waves in the sea. The resultsare however readily tranferable or modified for sound, waves in blood vessels and othertypes of General solution to wave equationRecall that for waves in an artery or over shallow water of constant depth, the governingequation is of the classical form 2 t2=c2 2 x2( )It is easy to verify by direct substitution that the most General solution of

Initial conditions that specify all derivatives of all orders less than the highest in the differential equation are called the Cauchy initial conditions. These conditions are best displayed in the space-time diagram as shown in Figure 2. 2 tt xx) t u=f(x u =g(x) u =c u t x Figure 2: Summary of the initial-boundary-value problem

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  Value, Problem, Initial, Equations, Waves, Wave equation, Value problems

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