normalizing sections of audio file

It sounds like you have re-invented the “dynamic range compression”.

The effect would need to be more sophisticated than you describe in order to achieve reasonable sound quality.

If you simply amplify (normalize) 10 ms sections, then there will be a click every time the amplification amount (“gain”) changes. To avoid the clicks, the gain would need to change progressively, so that when a quiet section is encountered, the gain is ramped up over a period of time. In a “compressor” effect, that period of time is called the “attack time”. When the input level rises again, the gain would need to ramp down over a period of time (the “release time”). In a “compressor” effect, the strength of your normalize function is called the “compression ratio”. If you are normalizing each 10 ms window to the same level, then that’s a compression ratio of “infinity:1”.

You would also need to not normalize sounds below a lower threshold, otherwise the noise in any “silent” parts would also be normalized. This lower threshold is usually called the “floor”.

See this topic: AGC - Automatic Gain Control
The best version of that effect is the one by Nicholas K in this post: AGC - Automatic Gain Control - #34 by Nicholas_K
The “manual” for the effect is in the first post: AGC - Automatic Gain Control

Instructions for installing the effect are here: Effect Menu - Audacity Manual