Is it normal to hear water noise in the house when turning on water hose after installing copper piping?

Yes to a certain extent. If you are drawing water in part of the home you usually hear a slight noise elsewhere. This is not a raqttle is it, just a slight hum?

Usually the noise is from cavitation in a valve.

Copper pipe lose a significant amount of heat to the air. As hot water passes through, the conductivity of the material pulls heat away from the water and then the air pulls that heat from the pipe which creates the noise.

Post says hose so I am thinking cold water. How would you explain cold losing heat and making noise.