Is it permissible for a woman to raise her voice at her children in public places, or while explaining in a university with students present, and what is the evidence for this from the Quran and Sunnah?

The majority of scholars are of the view that a woman's voice is not awrah (private/uncoverable), but it becomes impermissible if it involves softening the speech or leads to fitnah (temptation/strife). A woman must lower her voice when addressing non-mahram (definition) men unless there is a necessity or urgent need. As for a woman teaching in mixed-gender universities, it is permissible with Shariah-compliant controls, such as wearing hijab (definition), avoiding khalwah (private seclusion with a non-mahram), and refraining from softening the speech. However, it is preferable to avoid it to prevent fitnah.