MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF OCEAN ENGINEERING
13.811 Advanced Structural Dynamics and Acoustics
Second Half - Problem Set 1
Assigned: 5 Apr 2004
Due: 14 Apr 2004
Problem 1
Earl G. Williams Problem 2.3
Problem 2
Consider a 2-D wat
13.811 Advanced Structural Dynamics and Acoustics
Quiz - Acoustics April 21, 2004 Question 1. 1 ikz h p (x, y ; 0) = 2 e p (kx , ky , h)eikx x eiky y dkx dky 4 (4)
Question 2. x eikx0 x eikx0 x )= 2c 2i = k /2 = /2c. Insert into eq. 1 and use EGW eqn. 1.5
13.811
Advanced Structural
Dynamics and Acoustics
13.811
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS
Lecture 1
Fundamentals of
OCEAN ACOUSTICS
Figures in this lecture are from Jensen, F.B., W.A. Kuperman, M.B. Porter, and H. Schmidt. Computational
Ocean A
13.811
Advanced Structural Dynamics
and Acoustics
Acoustics
Lecture 10
Bessel Functions of the First Kind Jn(x)
Bes s el func t ions of the firs t k ind
1
n=0
n=1
n=2
n=3
Jn(x )
0.5
0
-0.5
0
2
4
6
8
10
x
12
14
16
18
20
Bessel Functions of the Second Kind
Coordinate Systems and Separation of Variables
1 2
Revisiting the homogeneous wave equation + 2
=0
2
c t
2
where previously in Cartesian coordinates, the Laplacian was given by
2
2
2
= 2+ 2+ 2
z
y
x
2
We are now faced with a spherical polar coordinate sy
Coordinate Systems and Separation of Variables
Revisiting the wave equation
1 2
+ 2
2 = 0
c t
2
where previously in Cartesian coordinates, the Laplacian was given by
2
2
2
= 2 + 2 +
2
z
y
x
2
We are now faced with a spherical polar coordinate system,
13.811
Advanced Structural
Dynamics and Acoustics
Acoustics
Lecture 4
13.811
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS
Lecture 4
Greens Function
U(t)
Helmholts Equation for
Greens Function
r
a
Proof
Greens Function
13.811
ADVANCED STRUCTURAL DYNAMICS AND
13.811
Advanced Structural
Dynamics and Acoustics
13.811
ADVANCED STRUCTURAL DYNAMICS AND ACOUSTICS
Lecture 2
The Acoustic Equation of Motion
Perturbation
1D equation of motion
Other Coordinates
Equation of Motion
13.811
ADVANCED STRUCTURAL DYNAMICS AND A
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF OCEAN ENGINEERING 13.811 Advanced Structural Dynamics and Acoustics Second Half - Problem Set 3 Assigned : 5 May 2004 Problem 1 Earl G. Williams Problem 6.16 Problem 2 Repeat Problem 1 for rigid sphere P
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF OCEAN ENGINEERING
13.811 Advanced Structural Dynamics and Acoustics
Second Half - Problem Set 2 Solution
Problem 1
Using equation (2.52) from text and substituting the expression for p(x,y,0),
P (k x , k
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF OCEAN ENGINEERING
13.811 Advanced Structural Dynamics and Acoustics
Second Half - Problem Set 2
Assigned : 15 Apr 2004
Problem 1
Earl G. Williams Problem 2.11
Problem 2
Earl G. Williams Problem 2.12
Due
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF OCEAN ENGINEERING
13.811 Advanced Structural Dynamics and Acoustics
Second Half - Problem Set 1 Solution
Problem 1
(a)
.
Using equation (2.99) of text and substituting wo for surface velocity,
.
.
W ( k
13.811 Advanced Structural Dynamics and Acoustics
Quiz - Acoustics April 21, 2004 Question 1. 1 -ikz h p (x, y; 0) = 2 e p (kx , ky , h)eikx x eiky y dkx dky 4 - - Solution Problem 1 Fourier transform of field at distance h p (kx , ky ; h) = Backpropagate