By Philip M. Morse, K. Uno Ingard (auth.), S. Flügge (eds.)

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**Sample text**

Bulk scattering. Suppose, at first, that" differs from zero only inside a sphere of radius a around the origin. 1) This approximate solution is called the first Born approximation. 30 PHILIP M. MORSE and K. UNO INGARD: Linear Acoustic Theory. Sect. 16. Suppose our incident wave is the plane wave eiT... , where a, is the unit vector in the r direction. The first Born approximation then is 'P(r) I(f},q;) ~ . ek, - eik, -,,-/(f}, q;), fff ei ... p· fff rox(ro)dvo- ... 2) (,ua<1) where p = k(a,- a,) =,u (a.

4). 35 Uniform impedance. Sect. 18. The single region we are to discuss in the present chapter is presumed filled with a fluid of density e· and sound velocity c. The acoustic impedance of the boundary surface at the point f'B is ec C(rB) = ec/{J (rB), where C, called the specific acoustic impedance (or sometimes just impedance) and {J, called the specific acoustic admittance, are point functions of f'B and of the frequency (ro/2'll) of the wave. I. Reflection from a plane boundary. 18. Uniform impedance.

If, however; the acoustic impedance of some part A of the boundary is not a point function of position on B then, as shown in the previous discussion of boundary conditions, we must analyze the wave in the boundary material" outside" that part of B. In other words we must solve the acoustic equations in another region H', which directly adjoins H along the surface A; H being on one side of A and H' being on the other. In these cases we can set up two integral equations, one for region H and the other for H', which coincide over parts of their boundary surfaces and which can thus be combined to obtain a solution in both H and H'.