DIAGNOSIS That's the sound of air getting pulled into the water line. The most common cause is a clogged or improperly seated inlet tube inside the water reservoir.
FIX Unplug the machine and remove the water reservoir. Look inside the opening where it seats onto the base—you'll see a small plastic tube (the inlet). Use a straightened paper clip or pipe cleaner to gently clear any mineral deposits or coffee grounds from that tube. Rinse the reservoir thoroughly and reseat it firmly.
IF THAT DIDN'T WORK The one-way check valve inside the base, which prevents backflow, might be stuck with scale. Descaling the machine with a vinegar solution might free it up.
HEADS UP Always use filtered water if you have hard water. Scale buildup from minerals is the enemy of any drip coffee maker's internal plumbing.