41 
The corresponding energy given to the piston and the entrained water of mass 
M' is then 
Amat )v" = 2Te'p, eee eee ooo eee eee eee (45) 
2 (M4of" )n 
This energy has ultimately to be absorbed by the spring resistance and 
is the energy communicated from the water to the target. 
406. For comparison with the previous infinite plate theory it is convenient 
to express the results in terms of unit area of the piston, If 
ee Ses ail = mass per unit area of piston oe. ee. (46) 
ae 
: MaM") v~ 
Q = 2 a2 = energy transferred per unit area of piston (47) 
C) P energy directly incident on unit area of 
U 2pen piston coe eee eee eee eve (48) 
then using equation 43 for M' it then follows from equations 45 to 48 that 
a a 
ae *a(=) | Ee | Mls fees: aise a 
In equation 49, the fraction 3itm/Bpa is always small for practical ratios 
of plate thickness to plate diameter. The main factor determining the 
magnitude of (1/Cl:is thus the ratio of c/n, the characteristic length of 
the pulse as given for example by equation AY to the plate radius a For 
a given target, that is given a, the ratio yan will increase steadily 
as c/n increases, that is as the size of the charge increases and there 
will be a particular size of charge for which = i- For larger charges 
giving longer pulses, the communicated energy{Y will become greater than 
the energy$l; in that portion of the pulse which is directly incident on 
the target. What happens physically is that the pulse striking the 
baffle round the piston or plate is reflected without any absorption of 
energy and the pressure in front of the baffle is higher than in front of 
the yielding piston, Equalisation of pressure then tends to set in by the 
formation of a diffraction wave starting out from the periphery of the 
piston This wave contributes an increase of pressure on the piston and 
a decrease of pressure on the baffle. In this way, some of the energy of 
the pulse incident on the baffle is diffracted on to the piston The 
diffraction of sound pulses of small amplitude in water is similar to 
diffraction in air discussed in Part 1 Chapter 4 of this Textbook 
where it is pointed out that long pulses are subject to greater diffraction 
than short pulses. This same effect is evident in the present problem 
and is responsible for the steady increases of § dwith increasing length 
of pulse. 
107. The preceding simple theory has been extended by a number of 
refinements of which the most important is the consideration of the effect 
of the compressibility of the water. The assumption of inconpressible 
flow implies that the water everywhere in contact with the piston knows 
immediately of the reflection of the pulse at the surrounding baffle and 
