How much difference does having a specific mouthpiece have?
I have an 11B4.
I understand what the different names mean but what difference does a deeper mouthpiece for example have on tone/resonance?
The trumpet mouth piece is made up of 4 main sections: rim, cup, throat and backbore.
All the following information comes from The Trumpet by John Wallace and Alexander Mcgraham, the Vincent Bach mouthpiece manual and my own experience as a trumpet player.
A thin rim is good for tone and control of articulation but cuts into the lip. A wide rim is better for endurance, as it spreads the pressure on a wider area. I've also that a wide rim is better for playing high but I've never seen an explanation for that.
The cup varies in a number of ways. A large diameter produces a rich tone and allows for louder playing but requires much more effort to play. A deeper cup darkens the tone and makes the lower register more secure whereas a shallow cup brightens the sound and makes the higher register more secure. The shape of the cup also varies - though I'm not sure of the effect. The Trumpet (see below) states that a v-shaped cup produces a dark sound and a bowl-shaped cup produces a bright sound, but in my experience the opposite is true. However, I've never tried two mouthpieces that vary only in cup shape.
A small throat strengthens the upper register, produces a brilliant sound and requires less effort whereas a large throat produces a richer, louder sound with less resistance.
The backbore is more complex. The Trumpet states that a steeper taper produces makes high notes easier and brightens the sound but Vincent Bach Mouthpiece Manual notes that the design of the backbore varies wildly and the effect depends on its interaction with the rest of the mouthpiece.
There is some amount of hard physics behind how different sections of the mouthpiece function but it is an enormously subjective field and the only way to work out the effects is to try a lot of mouthpieces, and ask other trumpeters why they use what they do.
Some advice for your case: the 11B4 is a standard beginner's mouthpiece, which I used for many years until I was told to get a larger one. I switched to a Bach 1 1/2C on recommendation and the difference in volume and tone quality was enormous. It's well worth switching to a larger mouthpiece when you can sustain the puff you need.