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and reflected beam Is 21. The impulse of tne diffracted pulse is - | (1 - @), Thus when 
O= 37 so that the wedge has such a wide angle as to become a single plane, the total impulse 
is 21. When @ = 0 so that the wedge is a semi infinite sheet the total impulse is 21-1 = I. 
It will be seen, therefore, that Friedlander's resolution of the apparent paradox with 
which this investigation started is that the total impulse of a pulse striking an inclined plane 
is always (1 + 24 |, where | is the impulse of the incident pulse. On the other hand, at points 
far from the vertex the pressure pulse predicted by the simple theory of reflection at an infinite 
plane scp rates from the diffracted suction disturbance, the intensity of which becomes ultimately 
very small though its pulse remains constant. 
When the incident pulse is not confined to a finite duration but extends indefinitely as 
does the exponential pulse represented by (1), the reflected and diffracted zones on the reflecting 
plane do not separate, so that the above discussion must be modified, A useful method for 
discussing the reflection of a pressure pulse of the type represented by (1) is to calculate the 
impulse of the part of the system where the pressure Is positive, Its initial value near the 
vertex is equal to | (1+ 2 ), for this is the value of the total impulse and it is found that near 
tne vertex no suction region is formed. At great distances from the vertex where the incident and 
refracted pulses have almost completely separated from the diffracted suction area, the positive 
pressure impulse tends to the limit 21. The ratio of the positive pressure impulse to its limiting 
value 21 at any distance from the vertex may be taken as a measure of the completeness with which 
the true reflected pulse has established itself at this distance. 
Figure 3 snows Friedlander's calculated values of 
ae positive Empaise on plane asvaefunctlonofi = t= distance from vertex 
impulse of incident pulse 1 c pulse length 
for the pulse represented by (1). Here the "pulse length" is defined as c/n. 
The calculations show the values for @ = 45° and @ = 15° and the results are plotted in 
Figure 3 with rn/c on a logarithmic scale. It will be seen that with a plane inclined at 45°, 
the reflected pulse is established to within 10 per cent. of its ultimate value when the Incident 
pulse has moved about 10 pulse lengths up the plane. 
; When tne angle of incidence is 15° the reflected pulse does not establish itself to this 
extent until the incident pulse has travelled a distance of 80 pulse lengths along the plane. In 
the first 10 pulse lengths the positive impulse has only risen from its initial value 1.081 to 
1.241. For smaller angles of incidence the positive impulse on the plane tends-to 1.01 near the 
vertex and the distance from the vertex at which there is any appreciable increase over this value 
becomes very great, so that in the limit when @ tends to 0 no reflection takes place. 
Reflection at curved surfaces. 
The reflection of pulses at curved surfaces provides a difficult problem. in two cases 
however, namely, the paraboloid and the parabolic cylinder, the solution has been obtained, The 
method, originally due to Lamb, has been modified by Friedlander, who finds that, unlike the case 
of the reflecting plane, the pressure-time curve is identical at all points on the surface. This 
is true for all kinds of incident plane pulse or wave and the total time integral of the pulse is 
simply 1, ise. the positive contribution due to the reflected and diffracted wave system is exactly 
neutralised by their negative contribution. If, however, the integral of the positive pressure 
alone be taken, the positive pulse thus found depends on the ratio c/nf, f being the focal length 
and c/n the pulse length. 
For very thin pulses this positive pulse is 2! and this corresponds with __~-*ate reflection 
of the ordinary type. When the pulse length is twice the focal length, i.e. c/n = ._. us of 
curvature of the parabolic cylinder at the vertex, the positive impulse is 1.31. For very long 
pulses the positive impulse is 1.01, Friedlander's results are shown in Figure 4. 
Reflection of a pressure pulse from a plate. 
Normal incidence. 
: When the: pulse is reflected perpendicularly froma plate which is not rigid and fixed the 
motion of the plate due to the combined action of the incident and reflected pulses gives rise to 
modifications ss... 
