199 
APPENDIX I | 40 
2. REFLECTION OF WAVES 
or 
wan | ad Ties aged Da 
Pic, Pic, P2lo 
Solving, P 
p= Poe, p, p= Polo — Pie) p 
iGhiaP Tes Pil) + Pele (7a,b] 
The reflection coefficient, or fraction of the incident energy that is re- 
flected, is : ‘ 
Et) (prcrseniey) [8] 
We note that everything depends 
upon the acoustic impedances of the medium. 
If these are equal (pic, = p2c2), no reflec- 
tion occurs. If pici< pec2, p’ and p have 
the same sign, that is, compressions are re- 
| 2 flected as compressions and rarefactions as 
rarefactions; if p1c1>pz2cz, p” and p have 
p,u opposite signs, so that compressions are re- 
flected as rarefactions, and vice versa. If 
ao ee c= 0, or if p,= 0 as for vacuum, R = 1, re- 
piu" flection being total. 
Some numerical values for waves in 
sea water reflected from various mediums are: 
R 
Figure 14 p/p 
1 - 0.0011 
- 0.99946 
1. OBLIQUE INCIDENCE 
If a plane sound wave falls upon 
a plane interface at an angle of incidence 
6 (Figure 15), the problem of reflection is 
easily treated provided one medium can be 
assumed to slide without friction over the 
other. Then, equating components of the 
particle velocity perpendiculer to the in- 
terface in the two mediums, we obtain 
Pp’ 2poc, cos 0 
P ~ pyc, 0086 + pic, cosd’’ 
BE" _ P2¢,008@ — pic, C08 6 [9a,b] 
P P2C,c08 8 + pic, C08 0’ Figure 15 
