How would I go about playing the normal Minecraft eating sound when I feed my custom tamed entity.

Use one of the World#playSoundXXX methods and insert a valid sound file name (open Minecraft's 'sounds.json' file to find valid sound names).

 

An example from inside an Entity sub-class that plays the xp orb sound:

worldObj.playSoundAtEntity(
this, // the entity at which to play the sound
"random.orb", // sound file name from sounds.json
1.0F, // volume (randomize if you want)
0.5F * ((rand.nextFloat() - rand.nextFloat()) * 0.7F + 1.8F) // pitch that has lots some randomness
);

Great thank you

Apparently it can't play the sound as it is unkown... I used this:

 

worldObj.playSoundAtEntity(this, "random.eat1", 1.0F, 0.5F * ((rand.nextFloat() - rand.nextFloat()) * 0.7F + 1.8F));

Delete the number!

Only random.eat.

Ohhhh... Hahahah thank you