How to broadcast audio over network so all computers are synced?

Anyone who grew up in the age of radio and had the kitchen and bedroom radios tuned to the same channel knows what I want to do.

I want to have a master broadcast computer and then be able to go from room to room and choose whether or not to put the computer in that room is playing that master channel. So then I could walk around the house and here the same music. Can the broadcast channel be used? I feel like this should be a solved problem, but Google is rather unrevealing.