65 
Ale Energy associated with pulse. The energy per unit area Q 
transmitted by the pulse across the spherical surface at radius r is given 
by 
Q = PEW Elo casi) jheles bases, hese! Uses: Meee) <sea/ (AIG) 
= 
The integrand in equation A16 is the rate at which work is done per unit 
= by the water within the sphere of radius r on the water outside this 
sphere. 
From the approximate relation of equation A13 and equation a8 
oS 00 
2 
OQ = ps pdt = 28 feces} ae See yectetemetects (417) 
a o 
The total energy E transmitted across the spherical surface of radius r 
is given by 
oO 
2 
B= 40 rQ = 2 | [-0} dt sid) Sea) en ae ee 
ce] 
The use of equation A13 in deriving equations A17 and A18 corresponds to 
neglecting the second term in equation Al1. If this latter term is 
taken into account, the energy E is no longer independent of distance, 
and even when the pulse is strictly finite in duration, some energy is 
left behind as kinetic energy of the water after the pulse has passed. 
