what is the term for the first sound the tom makes when the stick hits the drum and what affects it [. . .] on some drums it goes on forever and is almost electronic sounding,on some drums it goes on shorter and is low-pitch
You could be referring to a variety of things, but broadly speaking what you hear predominantly when you strike the batter head of a drum with a stick will be a
note - i.e. the head will vibrate at a certain frequency and that frequency will be an A or a G or somewhere in between. Notes are usually defined in relation to the concert or standardised pitch of A4, or middle A which is 440Hz.
Obviously, the situation gets more complicated when you take into consideration the fact that in addition to the vibration of the batter head, there will be the vibration of the resonant head (if the drum has one) and the shell of the drum itself. However, the pitch of the note coming from the batter head is what you're asking about and that is largely affected by the diameter of the drum. So roughly speaking a 10" tom will sound higher up the scale than a 22" bass drum. Other factors effect the overall quality or colour of the sound (something usually called
timbre). These are:
- The thickness of the batter head
- The thickness of the drum shell
- The angle of the bearing edge of the drum (i.e. how much of the shell actually makes contact with the batter head)
- The mass of the drum's hoops
- The mass of the drum's lugs
- The mass of the stick striking the head
- The shape of the tip of that stick
- Some would argue that the type of wood (or other material) that the drum is made of has some effect on the timbre of a drum as well
So, for example if you took two toms of exactly the same depth and diameter and with a batter head tuned to exactly the same tension but varied any of those things listed above - you could end up with very different sounding drums.
The additional thing you mention about some drums "going on forever" is
resonance. This basically means how long the note produced by the drum is allowed to be sustained and how loud the drum is. So, using the identical toms again, if you put a single ply head with triple flanged hoops and small lugs that sat near the edges of the shell on one and a two-ply muffled head with die cast hoops and lugs that ran the entire length of the shell on the other: the 1st would ring out and be big and booming whereas the 2nd would sound drier, focused, and perhaps more "electronic".
Hope this helps.