GEOPHYS 624
Homework 1
Due: Tuesday, Sep 28, 2004.
Problem 1: (total=30 pt) In the following figure (from the book). The left
of the string has density of 1 and right one has density of 4.
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
(1) (6 Pt) Find the seismic velocities of the two different string
segments by measuring the distance vs. time slope of the wave
pulses on the left and right sides of the figure. (Note: you can
draw on it, or blow it up by copying and use a separate page).
(2) (24 pt) For the top 3 time traces, describe in detail the wave
behavior of the two pulses. Make sure you discuss it in view
of 1. amplitude 2. polarity and 3. wavelength. Justify your
answers from reflection and transmission coefficients.
Problem2: For the stress tensor
2 1
3 


  1 1 2


3 2 5 
find traction on the
(1) (5 pt) x-y plane

(2) (5 pt) y-z plane
(3) (10 pt) the plane with normal (3,2, -1)

Bonus Problem: (5 additional points)
Both Juefu and Somanath asked in class whether we could use other
functions to express the eigenfunction of a “stringogram”. This is indeed an
interesting question worth investigation. We know that sin, cos and
complex exponentials can do the trick. The question is whether we can find
a solution that doesn’t involve any of the above. To make things easier,
think of a simpler, first order eigensystem,
U(x, )
 CU(x, ) (C is a constan t)
x
What is an alternative form of solutions to this system that do not involve
sin and cos. Will this solution that you propose satisfy the true eigensystem
of string modes and why?