20 





[8a. b, c] 



Here T„ is the time constant of the Incident wave, Tj, Is called by Klrkwood 

 the damping timt of the plate; If the plate. In contact with the water, is 

 given an impulsive velocity and then left to itself, its velocity decreases 

 in the ratio l/e = 1/2.718 in the time Tp, provided no forces act other than 

 those called into existence by the motion of the plate against the water. Tp 

 may be visualized as the time required for a sound wave to traverse a thick- 

 ness of water having the same mass as the plate. 



The time T. might be defined more generally, for any type of pres- 

 sure wave, as the time required for the plate to attain its maxlmip forward 

 velocity. It may be called the compliance time for the plate under the ac- 

 tion of the wave. 



In the case of the exponential wave, if r„ = T^, i = 1 and T„= T^ = 

 Tp. Thus the compliance time is the same as the damping time for a wave of 

 equal time constant. If T„ * Tp, the compliance time T„ lies between the 

 damping time Tp and the time constant of the wave T„. Thus for a very light 

 plate, Tf < T„ < Ty,; in this case the positive action of the wave on the 

 plate ceases while the wave is still strong. If Tp is much smaller than T^, 

 so that T is much larger than unity, the maximum velocity i;„ approaches 2pjpc 

 or twice the particle velocity In the incident wave. For a relatively heavy 

 plate, on the other hand, Tp > T„ > T„. As the plate is made still heavier, 

 both Tp and r„ increase without limit. 



As an example, for the shock wave at 50 feet from 500 pounds of TNT 

 exploded in sea water, p„ and a are of the order of 2100 pounds per square 

 inch and 1500 second"^ respectively. Thus T^ = 1/1500 second. The values 

 of the compliance time T„ for such a wave falling on steel plates of several 

 thicknesses are shown in Table 1 , together with the values of x and of the 

 damping time T, of the plates against sea water. 



TABLE 1 



