I have looked around a lot on this forum and it looks like there is a lot of people with various boost / turbo related issues. I apologize if this has already been addressed, I could not find the same noise issue. My truck is dropping boost at moderate acceleration and does it worse when its cold - below 32F.
I disconnected the blow-off valves so that it could be heard better on the video.
Thanks for any thoughts.

2012 F-150 3.5l

 

Check to see if you have any codes set. I had a single signal wire in the harness connector for the Turbo Charge Boost Pressure/Charged Air Cooler Temperature sensor break at the back side of the connector (right at pin). This wire harness comes from the top pf the engine and does about a 180 degree bend at the sensor. The sensor sits right in front of the intake and is easily accessible. The broken wire would cause intermittent loss of the signal the truck would loose power (drop in boost). It would not set a code as it was intermittent. The wire finally separated for a long enough period to set a fault for the sensor then I began troubleshooting. I removed/inspected/cleaned the sensor. I use my ohm meter to look for open circuits and failed components in the sensor. I used my Ohm meter to check out the wiring harness between the sensor connector and the ECU. I finally found a single broken wire right at sensor connector. I managed to disassemble to connector and repair the broken wire. This sensor provides boost pressure to the ECU and is critical to operation of the 3.5 L EB motor. A faulty boost signal to the ECU would cause the ECU to go into limp mode maybe resulting in the drop in boost pressure you are seeing.

Here is a picture of the sensor.

TCBP/CACT sensor