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*Transients*

Google ADSR - Attack, Decay, Sustain, Release. That's the parameters forming the envelope of sound.

Transients are... Better look that up, too ;-) I think I know it but want to avoid others to correct me, haha.
 
I think the term you are searching for is attack. The factors that affect attack are the stick tip/material/shape, size of the stick, velocity of the stick as it hits the head, angle of the tip as it hits the head, the drum head makeup itself, the tension on the drumhead, the tension on the reso head, your grip on the stick, your mood...there's probably more factors....all these things conspire to make each drummer sound unique.
 
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:

  1. The thickness of the batter head
  2. The thickness of the drum shell
  3. The angle of the bearing edge of the drum (i.e. how much of the shell actually makes contact with the batter head)
  4. The mass of the drum's hoops
  5. The mass of the drum's lugs
  6. The mass of the stick striking the head
  7. The shape of the tip of that stick
  8. 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.
 
i was talking about the thud when you hit,not the tone

like on prog/jazz guys drums the thud is long and high pitched but on some other drums the thud is short and low pitched like the batter hitting the bass drum
is it related to the note or resonance ?

Both: high/low pitch is the frequency or note, long/short is the resonance. So - in the example you gave - the 10" tom on your prog/jazz guy's kit has the batter head tuned tight and he perhaps has thin shells with a single-ply batter head and no muffling: high pitch with maximum resonance.

The "other" guy has his bass drum batter head tuned loose (sometimes it will be so loose as to be what is commonly referred to as Just-Above-Wrinkle point) and the drum has a thicker shell and most likely been stuffed with blankets or pillows or whatever to give that hard THUD bass drum sound that is very popular in pop/rock music: low pitch with minimal resonance.
 
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