The pulse grenade is a weapon that creates a large, crackling electromagnetic pulse, dealing only minor damage to biological creatures, but increased damage to mechanical targets such as robots and automated turrets. In addition, most robots are disabled for a few seconds by the burst, leaving them open to attack.
It is also possible to plant a live grenade on an non-player character by passing one from your inventory to the non-player character's inventory via pickpocketing. This will kill the non-player character, regardless of how much health or damage resistance they have (making the pulse grenade far more deadly against a single biological target) whilst other targets caught in the blast radius will only be dealt minor damage, in contrast to other grenades.
Considering its very low base damage, it is fairly safe to throw a pulse grenade at an enemy at point-blank range, as it will barely have an effect on you.
Six pulse grenades can be found in the Robot Repair Center in Frank's safe in the offices to the left on the first floor.
Four pulse grenades cane be found south of Wheaton Armory in an unlocked grenade box in the L-shaped raised hut near the Armory gate. (NOTE: at lower player levels, there may only be 2 grenades in the box)
Four can be found in the Evergreen Mills Bazaar. There is a bar to the immediate right of the entrance with two side-by-side refrigerators. Jump up on the shelves to look behind the refrigerators; they're in a small crate.
Three grenades are in the Vault 92 Living Quarters section, in the room next to Data Storage.
Three pulse grenades can be found in the Nuka-Cola Factory. They are on a shelf in the Storage and Mixing V.A.T.S. section, just behind the friendly protectron robot.
Three can be found in the equipment rooms of Vault 112, adjacent to the Tranquility loungers, but are locked by a computer that takes a science skill of 75 to unlock.