1 Kings 1:45
And Zadok the priest and Nathan the prophet have anointed him king in Gihon: and they are come up from thence rejoicing, so that the city rang again. This is the noise that ye have heard. And Zadok the priest and Nathan the prophet have anointed him king in Gihon: and they are come up from thence rejoicing, so that the city rang again. This is the noise that ye have heard.
Solomon was anointed king at Gihon and then publicly proclaimed as king. The rejoicing over his anointing caused the city to resound, and that joyful noise heard in Jerusalem confirmed that the succession had taken place. This anointing and proclamation thwarted Adonijah's rebellion. The event fulfilled God's direction that Solomon should succeed David.