I have never visited datacenters that large, but transformer substations can have an audible hum to them. Tests of diesel generators can also produce a bit of noise.
I'm fairly surprised that there aren't zoning laws that prevents datacenters from being built where people live. When we built a fairly small datacenter we had to place it in an industrial area with no housing and no offices.
There are zoning laws (barring anomalies like Houston). Datacenters are generally only built in areas zoned industrial. The problem is there’s often some type of residential construction on an adjacent residential-zoned parcel. The zoning usually doesn’t require any kind of buffer between the residential and industrially-zoned area.
> I'm fairly surprised that there aren't zoning laws
If that's surprising, you should look into how infamous the city of Houston's lack of zoning laws has made it.