When I run my upstairs bath tub or down stairs bathtub, noise(air) comes out in the pipes in my mothers granny suite that is attached to my house

When I run my upstairs bath tub or down stairs bathtub, noise(air) comes out in the pipes in my mothers granny suite that is attached to my house
Why does hot water run out of cold water tapes for a few minutes before turning cold

Why does hot water run out of a cold water tap for a few minutes before turning cold

why does hot water run out of cold water tapes for a few minutes before turning cold
The water setting in your pipes picks up the ambient temperature in the walls and comes out warm until it reaches the cold water from the source.

When I run my upstairs bath tub or down stairs bathtub, noise(air) comes out in the pipes in my mothers granny suite that is attached to my house
Are you on a pump or city water? Regards, Tom

When we bought our house. The water line laid on the ground, due to Cap Rock.
It was Hot. Trenching for a day and chipping for 2 weeks allowed waterline to be buried.
Now, water is cold? Where does your cold water run? Through Attic?