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3 First Order Wave Equation

Conceptually, a first order hyperbolic wave equation is the simplest wave propagation model. The characteristic solution [20] in the time--space domain for the homogeneous, constant velocity model is illustrated in Figure 2. The first order hyperbolic system, Equation 2, has an analytic solution, . The initial condition is and the slope of the characteristic solution is the media velocity c.

The sign of , of Equation 2 determines the propagation direction of the wave. If is positive, the wave propagates to the right. Bidirectional waves are a property of the second order hyperbolic wave equation.