。
As she was speaking, her tone grew more forceful.
Literal
She [topic-は] is-speaking while [in-に] tone [subject-が] became-strong.
~ているうちに means 'while in the middle of doing ~' and captures gradual change during an ongoing action. 語気 (ごき, 'tone of voice, force of speech') is a somewhat literary word. 強くなった shows the i-adjective 強い in its ~くなる ('become') form — the change happening during the speaking.