I was also worried about this.

In our basement there is a high guage (thinner) stainless sink, solid enough for what use it gets, that makes a fair amount of noise when water is run into it. Kind of a hollow/tinny sound. It is not insulated.

Our copper sink is thicker, 14g, and didn't come insulated (some do) so I sprayed a couple of cans of undercoat (for cars, from the car store) on it, letting it dry between layers. It's kind of a tar like substance that is not sticky when it's dry. The resulting sound is dull, minimal, and not annoying to me. I prefer the sound to my fireclay, but don't tell....