Warbling sound

Recently I noticed my car tend to make 'warbling' sound during acceleration, more notable when engine is cold. The noise is not present when the car is stationary. Once the car warmed up, the warbling sound persist but more muted, it IMO actually make the engine sound more aggresive, not sure if that's a good or bad thing :P

This warbling sounds seems to appear concurrently with this rattling/knocking noise that appear to come from below the dashboard whenever the car move from a stationary position, especially at an inclination, the noise only last for 1-2 seconds. My rough guess is some sort of bushing related to the transmission worn out? which also causes the 'warbling' noise during acceleration.

Anyone experienced similar issue with current or previous car?