1178 
a 
tog 
ct Sia Wy ire 
i B e aR, 
ful SS ey shi ret 
2 Py 2 Ro - 6 
R 
° 
x = 0, t2R/C (20) 
The integrals in (16) and (20) cannot be integrated in terms of known tabulated functions 
and can at best be expressed in terms of an indefinite integral involving also a parameter. 
Numerical evalution of this integral for all possible combinations of upper limit and parameter 
would be extremely laborious and it is thus desirable to consider what approximations are possible. 
let us put 
th t= heh Utes R/C ‘ 
. ct RA DR, 
Romie uaa (21) 
t' 2020 
Rc Ric a 
BAR, ci.) 2.8, 
na mna 
so that t' is the time after arrival of the incident wave at a point P of the plate andé isa 
Non-dimensional quantity defined by the same equation as in Report A. 
Now when t' and therefore { is small, 
3 + Rel rc? x? 
Vaan = Vee eRclret te Sree ty? ars (22) 
and thus if 
yeaa aa eee, a u (23) 
and are sma 
i a a 
and we neglect terms of these orders in (16) we obtain 
B . Ve Re Ye 
’ c . ‘ hi 
DL gem aoe e a at (24) 
2p. a 
o ° 
whence after integration 
= 1 = ne t’ - nt’ x =" "6 
mee Ged [<e ré | (25) 
Po abe Ae) 
which is identical with equation (23) of Report A. The approximate expression for v wil) similarly 
agree with equation (25) of Report A. 
Thus the solution given in Report A for an incident plane wave will hold as a good 
approximation for an incident spherical wave provided t" is smal) enough to satisfy the conditions 
(23) above. 
It is of especial interest to consider whether these conditions hold up to the time when p 
Changes from positive to negative since if so the solution and conclusions of Report A for the case 
where the plate leaves the water will hold with sufficient accuracy for the spherical wave case. 
Now the time at which the water leaves the plate for an incident plane wave is from equation 
(26) of Report A given by 
nen, Lage (26) 
ANd soon 
