60 Hz is the AC power frequency in some countries.
That means the source could be lights (they have them in supermarktets, lots of them), fridges, airconditioning, basicly every thing that uses power could be a source of interference.
For this balanced audio is designed, so at least the cables won’t pick up the noise.
However, a humming deice with no electronic interference makes sound, so if you mic picks up that you have the wrong mic for the job.
Now, of course your phone does not let you hear this, 60 Hz is very low, the speaker is probably not able to playback a frequency that low.
So, now you know why there are dedicated sound guys who bring 10K worth of equipment to do a job like this.
I’m not saying that that is needed for such a job, but shooting something with too cheap equipment / not enough known how is not the way to go. Having to do a lot of work in post that never give you as good results as that you would have gotten in the first place makes it more expensive than doing it right the first time.
Bouke
http://www.videotoolshed.com