No, it's not like you say. 声の凄さ is the part where the voice is described as great. 知るべき means "(you) should know/understand".
My understanding by reading this sentence without context, is as follows: someone (the listener) has a great voice but maybe he/she is not aware/underestimates his/her ability. Therefore, the speaker tells him:
You should know/understand more (be more aware of) the
greatness of your own voice
Basically the speaker is telling someone that he/she has a great voice but doesn't seem to realize it.
You should look more into べき, for example here. In two words, is a way of expressing "should" in English.
The basic construction is: Verb-dictionary form + べき/べきだ (with exception for する => すべき/するべき).
Simple example: 約束は守るべきだ (you should keep your promises).
Final note: the ending さ is a colloquial way to make a statement more assertive. See for example this question.