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The inadequacy of the simple theory to represent the reflection conditions of a fixed 
finite plate may be seen by imagining the angle of incidence of the pulse to decrease to zero. 
As long as there Is a finite angle of incidence the pressure on the plate is according to the 
simple theory twice the pressure in the pulse. On the other hand, when the pulse is travelling 
parallel to the plane it Is undisturbed by it so that the pressure on the plane is equal to that 
in the pulse. This apparent discrepancy or paradox is resolved when the reflection of a pulse 
by a finite plane or wedge is considered. The change in a special type of pulse (chosen because 
it closely resembles the pulse produced by a submarine explosion of a high explosive charge) when 
it is reflected from a symmetrical wedge, the angle of which is 2 @, has been calculated by 
F.G. Friedlander. This pulse is a sound wave in which the pressure is zero till the arrival of 
shock wave in which the sudden pressure Change is Po The pressure subsequently dies down 
exponentially so that the pressure p at time t after the onset of the wave is 
p= poe (4) 
This pulse has a characteristic length 1 = c/n, (where c is the velocity of sound), in which the 
pressure dies down to 0.368 of its maximum value. The reflected wave ang the pressure on the 
wedge is proportional to p, and Is a function of 0, r/l and n (t — fest) where r is the distance 
of any point on the surface of the wedge from its vertex. The characteristic features of 
reflection by a wedge can be appreciated by reference to Figure 1, which shows the form of the wave 
fronts of the incident, reflected and diffracted waves. In Figure 1, 0 is the vertex of the wedge. 
The wave strikes the wedge symmetrically, the angle of incidence on each face being 90° -@. The 
line A 08, is the position of the wave front at the moment of striking the vertex. After a time 
r cos Bk the incident wave front consists of the two parts Aye, 0,8 above and below the wedge. 
The reflected wave front consists of the lines C e O,F, which are tangential to the circle 
described with centre 0 and radius 0G = OC, cos & = r cos @. The wave front of the diffracted 
disturbance is the part of the circle of radius r which lies outside the wedge, i.e. the segment 
HE, KF, LG. 
Assuming that @ < 90°, points on the wedge are reached first by the incident wave. In 
the section C,H the pressure is double that due to the incident wave. The section OH is subject 
to the rear parts of the incident and reflected wave and also to the diffracted wave which is a 
suction wave when the incident wave is a pressure wave. 
The time interval between the arrival of the wave front at the point C, and the arrival 
of the diffracted wave is (1- cos @)r/c. If therefore the incident pulse is limited so that It 
has passed any given point in a time interval T after the passage of the wave front, then it, Gas: 
greater than c T/(1 - cos @) the whole of the incident and reflected waves will have passed the 
point Cy before the diffracted wave reaches it. At points further away from the vertex than 
c T/(1 = cos 9) the pressure-tlme curve is as shown in Figure 2b, which shows the distribution 
for a square-topped pulse, i.e. an incident pulse in which the pressure suddenly Increases by an 
amount p, and remains at this value for time T when it suddenly returns to its initial value. 
As the wave proceeds the incident and reflected pulses remain constant in height but get further 
away from the region of the diffracted disturbance. The diffracted disturbance continually 
decreases in intensity but increases in the area covered, since it extends over the whole radius 
from the vertex to the diffraction wave front. Figure 2b shows the pressure-time curve 
calculated by Friedlander at distance 4 pulse lengths (i.e. 4c T) from the vertex of a 90° wedge. 
Figure 2c shows the pressure-time curve for a point 10 pulse lengths from the vertex. The 
reduction of intensity In the diffracted wave as distance from the vertex increases may be noticed. 
At points nearer to the vertex than c 7/(1 - cos @) the incident and reflected waves are 
not separated from tne diffracted wave. -At such points the pressure-time curve is as shown in 
Figure 2a, which represents the state of affairs at distance r= 5c T from the vertex. 
Friedlander has proved some interesting properties of the diffracted pulse. He shows for 
instance that its total impulse, (i.e. ie fr) (diffractea wave) dt) is constant at all distances 
from the vertex. 
panther. he finds that this constant is definitely related to the angle of incidence of 
the pulse 5 — a. lf the impulse of the incident wave is | where | = fF P; dt and P; is the 
pressure in the incident wave, the impulse applied at any point of the surface by the Incident 
AND sever 
