As a prospective PhD student, is it bad that I have interests in multiple areas of my field?
5th-year phd student, soon to be postdoc here.

The perception that anyone in academia has a laser-tight focus is not correct. In my experience, most of the people have rough idea of the field, and then stumble or got assigned a project that interest them well enough. Never feel guilty for not knowing exactly (or not having) specific interest, nobody does.

As a phd student you will have to learn a lot of new stuff, so having different interests is a plus as most of the work is interdisciplinary anyways.

That being said, when you join department, you will be expected to rotate in several labs (usually) in order to find best fit. In that process you might find out that best fitting lab is neither PTSD nor language-processing one, and that's entirely OK. Remember: you will be signing up for 5-7 years of work with a specific PI, not a topic.