1504 
4.5 The purpose of this alternative development has been to 
show that the distortion of an acoustic pulse on oblique reflection 
can be treated directly as a boundary value problem without 
recourse to the initial harmonic wave treatment developed by 
Rayleigh? and described in section 2. The phase angleZE defined 
in equation (47) can a posteriori be identified as the phase shift 
which is applied to the Fourler spectrum components of the 
incident pulse, but it is not a priori introduced as such. 
4.6 <A few remarks may be made at this point concerning the 
pressure field, Q , in the bottom. An exvression for /, may be 
obtained in section 2 by combining equations (7) and (9) or from 
the treatment in this section by combining equations (40), (51), 
and (56). In either case, one obtains the form: 
cos E Go)" 900) exp Jean + gale) Fifa) Be hess 
RS 
Ui] 
2cow*é (2m) “pe exp [ew Bote duo 
lee (2m) A Pe! B(w) exp [éwu 4 joy (deo 
ate) 
where Y is identical with the quantity? pp defined in section &. 
It will be seen that the integrand in the 
expression for P is not analytic because of the presence of the 
~- 28 = 
