in equation (6.14). Also for typical values of o , Tt , andT, 
the finite wave groups in equation (6.4), are essentially zero 
outside of the interval nr - Y/2<t<nr + ‘2. It then fol- 
lows that an adequate representation for equation (6.4) is given 
by equation (6.14) by simply chopping off the infinitely long (in 
time) function given by equation (6.12). 
Equation (6.14) is a sum of terms each of which is similar 
to the finite wave train studied in Chapter 5. The apparent per- 
iod of the wave is given by ‘/m, and if pt + ‘1/2 is equal to 
an integer, say, q times ‘/m, the results of Chapter 5 will apply. 
(Note, q ‘/m corresponds to nT of Chapter 5.) Equation (6.15) 
then yields equation (6.16) which shows that q is an integer if 
m is even. 
For even values of m, then, equation (6.14).can be expressed 
as the first condition of equation (6.17), and for odd m, the second 
expression can be applied. The results of Chapter 5 apply directly 
to each of the terms in the sum for even m. For odd values of n, 
a problem similar to the one solved in Chapter 5 would have to be 
solved. Formulated in terms of the notation of Chapter 5, the 
problem would be to find 7 (x,t) given that 7(0,t) = A sin 2nrt/T 
for -nt - 1/2 <t<nT + 7/2 and 7(0,t) = O otherwise. The solution 
can be found easily by the methods employed before, and the re- 
sults are not essentially different from the results of Chapter 5. 
The finite regular train of wave groups is therefore composed 
of a sum of finite wave trains of amplitude, a? and period, Pim 
Each train recuires (2p + 1)T seconds to pass the point x equal 
to zero. 
The forward edge and the trailing edge of each train advance 
= Aloe) = 
