CHAPTER IV 



DISCUSSION 



Results 



The equations developed for o) , o, and H in Chapter III for the new model can be considered to be 

 accurate within ten percent only for the parameter ranges given in Chapter II. The ranges of E;, for which 

 exact values are not known, and s, which may be varied, were extended beyond the limits of present 

 available data. However, the largest values of a, u), and P^ used in this model are not beyond the range of 

 possible values. These limitations were imposed by the assumption that k 2a a is small. This required that, for 

 the error caused by using just the first term of the spherical Bessel function expansions to be less than ten 

 percent, 



coa < 2.4 x 10 4 cm/sec. 



The limitation of k 2a a being small is a factor in all the previous models, but in most cases it is not mentioned 

 or, if it is mentioned, no limiting value is given. 



The range of E, utilized in the solution of the new model was 



1 poise < E, < 10 4 poise. 

 However, a more likely range of E;, as shown in Appendix A, is 



50 poise < E, < 2 x 10 3 poise. 

 This narrower range will be utilized in the remainder of the discussion because it results in a simplification of 

 equations III-26 and III-34 without, in all probability, affecting the results. Equations III-26 and III-34 simplify 

 to 3v P ?«! 



Uo 2 a 2 = iMow + ^l(3 Ya - 1 ) (IV-1 ) 



KOf V0t d 



2 



and 4 na 2 (-PA 



o = VPot ; , (IV-2) 



LU)2H2 ^ 0)2 ) \ 



respectively, when the upper limit of E, is reduced to 2 x 10 3 poise. A and K are negligible compared to 1 for 

 E,< 2 x 10 3 poise. A and K were the only remaining terms which contained b. Thus, for the a/b range given 

 in Chapter II, b is unimportant for £;< 2 x 10 3 poise. 



Figure 2 gives co a as a function of depth and surface tension, calculated from equation IV-1. s has 

 essentially no effect on u> a for s/a < 10 5 dyne/cm 2 at any depth and for s/a < 10 6 dyne/cm 2 for depths 

 below 1 00 m. For s/a values around 5 x 1 7 dyne/cm 2 , pressure has essentially no effect on o) a for depths 

 less than 100 m and at a depth of 1000 m, co a is increased by only 50 percent over its value near the 

 surface. 



At resonance, 



a = 4na 2 Q2 ( Po »\ (IV-3) 



V Pot / 



and 



Qrad = 



Pot 

 PofC w 



Pow^oa 



(IV-4) 



and 



Q v , s = ^P|£L _ (|V-5) 



q) *a / 2p 0a c Pa \ * / ,_2s\ - 

 ,h ~ 3( Ya - 1) V ~) V "P^T^J (IV-6) 



Thus, a is proportional to Q 2 at resonance. 



23 



