224 



36 



y Equation [60], and, lastly, the "extinction coefficient" 



ac __ a\ 

 D 2tt 



.65] 



/here \ is the wave length of the incident waves in homogeneous water. Then 



^-0'=l+fN^ 



1 - 



/ (^^2 3 w« 



;66] 



20-^ = V3 fN 



'1 - -<f + ^ 



N' w„ 



= y 



:67] 



The values of c' and of /? can also be written separately in terms of the 

 quantities denoted by X and Y as 



= c(ix.i,/5FTl^)-^- 



= |(ix+ivT^-r7^ 



[69] 



p, 



COEFFICIENT OF REFLECTION 



Suppose that, under the condi- 

 tions specified in the foregoing, a train 

 of plane sinusoidal waves in homogeneous 

 water falls at normal incidence upon the 

 plane face of a layer of uniformly bubbly 

 water. Then there will be a reflected 

 train of waves in the homogeneous water 

 and a transmitted train in the bubbly wa- 

 ter; see Figure 9- The pressures and par 

 tide velocities in these three trains 

 may be written as follows, in the notation Just employed: 



Incident: p = Pj cosw (* - - 



Reflected: p = p„ cos oi it + - 



Figure 9 - Sketch illustrating 



the Reflection of a Wave 



from Bubbly Water 



pc 



Transmitted: 



P3 

 Is. 



cos 0) (t - ^ + r'j 

 cos u (t — ^ + 



-P. 

 pc 



■) + ^^ sin 0) (t 



