In the Music & Sound Options tab, you can slide the "Players" sound bar all the way to 0%, which will mute the sound effects of eating. However, at the very last moment after having eaten something (at the same time that the hunger bars actually get replenished), a very abrupt clip of the sound will play for a fraction of a second. This seems unintended, and my guess is that a separate split-second sound clip may play in reaction regards to the hunger bars themselves filling, and that this split-second sound simply isn't classified to the "Players" sound bar slider.