MULTIPLE REFLECTED WAVES 93 



than doubles, and so on. At great distances from the source (for example, 

 four times the depth of the reflecting boundary) there is little difference 

 in intensity between waves repeated a different number of times. In this 

 case the modelHng was done with an emitter and a detector which did not 

 possess acute directional qualities. 



This is borne out by the theoretical calculations (Figs. 8 and 9) and is 

 explained by the dependence of the reflection coefficient on the angle of 

 incidence, namely, the greater the number of multiples, the slower does 

 the angle of incidence change with distance from the source and the slower 

 does the reflection coefficient change. Modelling multiple waves in a case 

 of a thin reflecting layer shows that when the distance from the source is 

 large, the curve representing the damping of the multiple waves as a function 

 of the number of multiples sometimes has a wavelike form (Fig. 11). 



Damping increases as the number of multiples increases, in inverse ratio 

 to the difference between the wave resistance in the reflecting layer and 

 the wave resistance in the covering medium (Fig. 11); and in the case of 

 a thin reflecting layer, also in inverse ratio to the difference in wave resistance 

 between the covering medium and the underlying layer. 



In some cases the refraction coefficient first increases with the angle ol 

 incidence, reaches some maximum and then decreases. This effect not 

 only reduces the damping of the multiple waves in some sectors of the 

 observation hne, but also in certain cases, causes their intensity to increase, 

 with distance from the source. With some slight difference in wave resistance 

 and in the travel velocities of the waves in the media covering and underlying 

 the reflecting boundaries, for example, multiple waves can increase in intensity 

 up to a certain distance from the source. This is implied in the foregoing 

 formulas and is shown in Fig. 9. 



The relationships we have indicated are to a considerable extent connected 

 with the absorbent properties of the media lying between the reflecting 

 boundaries. Multiple waves were therefore modelled under conditions in 

 which water, marble, paraffin, plastilene, were used as the covering media, 

 and the absorbent properties of real media must he within the range of the 

 absorbent properties of these models. Despite the wide range of the latter, 

 quahtative confirmation of the dependence we have indicated was obtained 

 from the modelling, but the quantitative ratios varied. 



We may note that the relationship between damping and frequency is 

 connected with the absorbent properties of the media. The damping of 

 multiple waves consequently depends on the prevaihng frequency of the 

 vibrations, and in the case of strongly absorbent media must be more 

 pronounced with relatively high prevailing frequencies than with low ones. 



