Meaning of "nearby" and "in close proximity"

I would really grateful, if someone let me know whether it is feasible to use "nearby" or "in close proximity" to talk about people who are near the point of talking. In the following sentence what I needed to say was mobile phones should be banned if it might pose negative impacts on surrounding people or people who sits next to phone users. Therefore, could someone please let me know whether the following two sentences are correct in terms of grammar.

However, the author of this essay contends that such devices should be banned only if they disturb others nearby.

However, the author of this essay contends that such devices should be banned only if they disturb others in close proximity.