The noise you are hearing is coming from the front wheel vacuum hubs. There is a TSB ( Technical Service Bulletin) regarding this condition and you will need to replace the solenoid mounted on the firewall near the battery. The new solenoid has a plastic cover over it to prevent the water from getting into it.
Some 2004-2006 F-150 and 2006 Mark LT 4X4 vehicles built before 4/24/2006 may exhibit a noise inXXXXXfrom the front Integrated Wheel Ends (IWE) and/or the 4X4 system being inoperative. The IWE solenoid may have ingested water and passed it to the IWE system causing water contamination in the vacuum portion of the system. A shorted IWE solenoid can set the codes C1979 and C1980. If either code is present, the 4WDH light will be inoperative.
Use the following Service Procedure to check and repair the 4X4 system.