COMMENTS ON FOURTH PROBLEM SET - FALL 2002

	In the assigned reading, you'll find that French's
presentation, while addressing indentical material, is quite different
from B&B's.  It can't hurt to read both and compare, and synthesize
the presentations for yourself.
	For instance, B&B give the p-V relation for adiabatic
expansion in Chapter 1, but no derivation.  French gives an
unconventional but excellent exposition in "The Elasticity of a Gas,"
Pages 176-178, that does not make any reference to thermodynamics
aside from that implied in Equation (6-20) on Page 177.  I've put a
link to some notes of mine from 18.023 on my 8.03 page.

	Problem 4.2 (B&B 2.4):  In order to do this rigorously (part
(c) needs a symbolic answer), you'll need either the result of B&B 2.3
(which is not assigned) or French Page 257.  Or rederive the
expressions.

	Problem 4.3 (French 6-2):  I get the answers in the back, but
you need to interpret them.  The subscript "A" is for the string, "B"
is for the discrete masses.  Hence, "nu_1" is the lowest frequency for
the string.

	Problem 4.4 (French 6-11):  For part (b), a little math and a
bit of reflection give the result suggested in the parenthetical
comment.  Or, if you're really familiar with Fourier series, you know
how to derive the result with more math.  This makes this a typical
French problem.
	(NOTE:  It is indeed possible to do this without using Fourier
Series, which is why it can be assigned now.  Fourier Series are on
the way.)

	Problem 4.5 (B&B 2.5):  No big deal, it's just that there's a
"kappa" and a "k" in the same problem, and if your handwriting is as
bad as mine, you gotta be careful.