Suppose we have a sound composed by many basic waves,which are described as known functions of time

How i can determine the amplitude of the final sound at a certain time t?

Perhaps i have to sum the amplitudes of all basic waves at time t?

if so,have i also to check that the sum doesn't overcome a maximum value,or goes under a minimum value?

for instance,if i use 16 bits for the amplitude (signed),and the absolute value of the sum is greater than 2^15 - 1,i have to take 2^15 - 1 if it's positive,and -2^15 if it's negative