How do I convince professors about my research interests?
In my experience (North American research-intensive universities) and point of view, this is a good question without a hard-and-fast answer.

having a specific research topic in mind is good in that it indicates that you've made an effort to think about the topic. However:

new researchers (undergraduates) often have very unrealistic ideas about what constitutes a practical research topic, especially for a beginner in the field who will have a limited amount of time to work on the project;
even good research topics may not fit in well with the specific research program of a particular researcher. As researchers are often supporting master's students from grants, their students' projects need to fit into the scope of the grant.
researchers (and fields) vary hugely in the amount of independence they give to (or expect of) master's students. You might be able to get some ideas about a particular researcher's approach if you can track down masters' theses of their previous students and look at the range of topics covered.



It's fine (and probably best) to say &quot;I have the following ideas about new projects I could work on ... but of course I would be happy to work on new or existing projects in your lab ...&quot;

similarly, it's good to express some knowledge of/interest in the potential supervisor's field. HOWEVER: I get a lot of e-mails that say something along the lines of &quot;I'm fascinated by your work in XXX and YYY&quot;, where XXX and YYY are topics that can easily be picked off of my web  page or a glance at my CV or Google Scholar page.
The most compelling aspect of an application/e-mail is evidence that a student has previously engaged with something about the subject. Even if you haven't done anything in the particular field, it  helps a lot if you highlight things that you know/have done that will make you well-prepared for research in the topic — this could be course projects you've done in related fields, or courses you've taken (or things you've taught yourself) that are good foundations for getting started in the field.

I appreciate that the last point is hard if you're just entering the field for the first time, but talk is cheap: demonstrating that you've already taken some steps to prepare yourself is much more convincing. If you can't do that, then demonstrating some awareness of which aspects of your current training would be useful is helpful.