Ill -8 



If gh^ = 1, the mechanical impedance of the fluid sphere becomes 

 identical with that of an equivalent sphere of water, since the impedance of a fluid 

 sphere to a "breathing" mode of motion* is 



3 PoCo' 



iatw 

 And indeed, the breathing mode in (III- 15) vanishes when gh^ = 1. 



The second term in (III- 15) corresponds to a "sloshing" type of motion, 

 due to the pressure differential across the sphere. The pressure across the sphere 

 is not quite constant, and the resultant force on the sphere causes it to oscillate as 

 a rigid body along the polar axis. Since the density of the fluid sphere differs from 

 that of the surrounding water, the amplitude of the resulting motion of the sphere 

 will be different from what a corresponding sphere of water would experience sub- 

 ject to the same pressure gradient. As a consequence, the fluid sphere will oscil- 

 late as a rigid body relative to the surrounding water in the direction of the incom- 

 ing wave. The normal velocity of this motion at the surface of the sphere depends 

 on 9 as cos 6 ; the pressure wave that is emitted will therefore be of the form 



ikr-iuut 

 cos 9, which corresponds to the second term in (III- 15). Note also that 



this term vanishes, as it should, when g = 1, i.e., when the mass densities of 

 the fluid and of the water are the same. 



A number of qualitative conclusions may be drawn from (III- 15). 



1. If gh^ << 1, i.e., the fluid sphere is much more compres- 

 sible than water, the breathing term completely dominates 

 the sloshing term and isotropic scattering results. 



*This may be seen as follows. The overpressure in the fluid sphere is related to 

 the "overdensity" according to (III-2a), i.e., p = co^ p . The change in volume 

 resulting from a normal velocity at the boundary relates the "overdensity" to the 

 boundary velocity according to 



3po 



P = - — U = -lUDp 



t a 



3 p ' c ' ^ 

 for harmonic motion. Substituting one in the other yields p = ° ° 



iauj 



as the linear relation between the harmonic driving velocity and the resulting 

 harmonic pressure. The constant of proportionality is the mechanical impedance, 

 where we make the analogy with electric networks by associating "velocity" with 

 "current" and "pressure" with "voltage." 



Arthur Jl.littlcjnt. 



S-7001-0307 



