What time did this occur? We can go back and listen to the archives to hear the beep you mention.
In Phoenix, several agencies transmit an audible tone about every 10 seconds during an emergency situation. They call it a "hot tone". It is used to alert users to keep the channel clear for only emergency traffic. I'm not sure if Omaha uses this feature, but that is my guess without hearing it.
When OPD or DCSO "clears the air for emergency traffic only" there is a beep that is transmitted about every fifteen or so seconds. This reminds everyone that the air is cleared. Some unit will request to clear the air without the beep, this is usually when they are serving a high risk search warrant.
They air gets cleared by a request of an officer, the dispatcher determines it needs to be and when an officer arrives at a priority 1 call or a crime in progress/just occurred call.