Re: how does the size of a drum affect the pitch or sound that comes out of it.

From what I have found, the size of the drum is one of three factors that 
effect the sound a drum makes.

For a basic text on why anything vibrates like it does, I would recommend:
Vibrations and Waves by French. It was my undergrad text and deals with the 
general background behind vibrating strings, rods, plates etc. It has some 
nice pictures of vibrations as seen when a metal sheet with sand on it was 
placed near to a speaker emitting a sound.

Anyhow, on to the question. I found the book, The Physics of Musical Sound, 
by Jess J. Josephs to contain exactly what you were asking.

To paraphrase: The fundamental frequency emitted by the drum is determined 
by f=2.405*(T/m)^(1/2)/(2*pi*r), where T is the tension of the drum skin, m 
is the mass per unit area, and r is the radius of the membrane.

Essentially, the larger the drum, the lower the fundamental (base) 
frequency emitted. However, as you can see, the type of drum skin, and how 
tense the skin is plays an important role too.

The drum will also emit 'overtones' as well as the fundamental, and these 
occur at 2.295*f, 3.60*f, 4.90*f, etc... So the note actually heard is a 
mix of the fundamental and the overtones.

Finally, there are 2 examples given, one of a kettledrum used in 
orchestras, and one of a bass drum.

The bass drum is said to have no definite pitch.
The kettledrum however can be tuned over a range of tones. This is done by 
varying the tension of the skin using turnkeys set all around the edge of 
the drum. (Note: You can see how tricky it would be to make the drum have 
the same tension all over the skin, as it is so large, and there are so 
many keys to turn. It's added to my respect for percussionists.) 

I hope this answers your question. Thanks.