DYNAMICS AND KINEMATICS OF SUBMARINE CABLE 1189 



where 



Ci = EA/pa, 



C-1 = Ta/pa . 



For non-zero Wa and a 7^ -w/'I, (85a) cannot be satisfied. This is a conse- 

 quence of the assumption of ^o = 0. With poa = 0, equation (b) impHes 

 in turn that To = constant, which agrees with our model. For the sub- 

 merged part of the cable, the equations do not yield a constant Tq and 

 thus contradict the assumed model. However, on the assumption that 

 the transverse motion is confined to a region near the surface, we con- 

 sider To to be constant in the submerged part of the cable as well. We 

 thus arrive at 



Tjiff — brm — yr]it — t-. riut = (a) 



(b) (87) 



7?ir'?i!-f , (^) 

 where 



as the differential equations governing the motion of the submerged 

 cable. The constant Ci is the velocity of propagation of a longitudinal 

 wave in the cable, while the constants C2 and C2 represent the propagation 

 velocities of a transverse wave in air and w^ater respectively. 



D.3 Solution of the Perturbation Equations 

 We write 



p(0, t) = IMt) + Prit), 



5(0, t) = Q,(t), 



and take as boundary conditions 



