REFRACTED AND REFLECTED LONGITUDINAL WAVES 



25 



7ref 



7ref 



Co(nn)"(^o'^o')"-^ sinaocosoo 



471; (Ao + 2^0) ^0, p r 



CoiPoPoriPo'Po')"-^ cos^ao 



4jr {Xq + 2/i(,) t;o, p 2n/?o - /?sd 



(8) 

 (9) 



Here /?q is the thickness of the upper layer. 

 For muki-layered media, the muhipher 



sin ocq 



l/'[S 



hi tan oci 



COS^ (Xi 



tan 



'sd- 



COS' 



aoJ 



from formula (3) can also be simplified and represented in the form 



smao 



when the angles at which the reflected wave under consideration strikes the 

 intermediate interfaces are not too great. The permissible error -with such a 

 substitution lies within the limits shown in Table 3, where Xj is the largest of 

 the angles (x^ (where i = to ?i — 2) at which the ^vave reflected from the 

 n — 1th and nth layers strikes the intermediate interfaces. 



Table 3 



It can be seen from the table that if ocj does not exceed 25° the permissible 

 error mil not exceed 9%. This degree of error will occur if all the angles 

 (X^{i = to n—2) are equal to 25°. If however some of them are smaller 

 than 25° the error will be reduced. Here the true values of the multiplier 

 ^ve are dealing with are lower than the approximate values. If, by analogy 



nil- 1-11 sin an cos ao . , . 

 with a two-layered medmm, ^\e substitute the value tor tms 



multiplier, we obtain still better accuracy. 



If the angles of incidence onto the intermediate interfaces of multi-layered 

 media are not too great, then the multiplier 



/^&^ 



sinoco 

 tan oc; 



~h. 



cos' OCi 



sd- 



tan (Xq 

 cos^ (Xq 



