Determining the initial and final amplitude

[Note: this section can be skipped on first reading.]

How do you determine the initial (or the final) dynamic? By determining the greatest difference between amplitudes in a state.

In the initial state, the greatest difference of amplitudes is between elements 1 and 2, 10000 and -10000, so

10000 - -10000 = 20000

The difference is 20000. That can be translated into decibels by

20 * log₁₀(20000) = 86.02 dB

So the initial dynamic is about 86 dB.

Let's say you wanted a final dynamic of 60 dB. What is the greatest difference in amplitudes you must have?

To translate dB into amplitudes, use the following formula:

amplitude = 10^decibels/20

1000 = 10^60/20

So if you want a level of 60 dB, you need the greatest difference to be 1000, which is 500 to -500.