ECE 473
Homework Assignment #3
Due: Friday, September 9, 2016
1. A string of density 0.0200 kg/m is stretched with a tension of 1.28 N from a rigid support at x = 0.55
m to a device producing transver
Homework # 3 Solutions
1. (a) /2 = 0.10 m or = 0.20 m
1/2
1/2
1/2
c = (T/L) = (1.28/0.02) = (64) = 8 m/s
f = c/ = 8/0.20 = 40 Hz
F sin k ( L x )
cos t
kT
cos kL
with k = 2/ = 2/0.20 = 31.4 rad/m
kL =
ECE/TAM 473
Homework Assignment #1
Due: Friday, August 26, 2016
1. Let x e t ( A1 cos t + A2 sin t ) . Show
that x ( t ) Ae t cos (t + ) . Evaluate the constants A and
=
=
in terms of A1 and A2 , the
(7.8) Simple Line Array (N sources)
kL
Recall for an in-phase line source, H ( ) = sinc sin
2
z
y
L
x
r
p(r,t)
Now, consider N point (simple) sources, each with same source strength and phase, and
(7.4) Radiation from a Plane Circular Piston
The plane circular piston is of particular interest in acoustics because it is a model for a number of
sources, i.e. loudspeakers, open ended organ pipes,
Chapter 7 Radiation and Reception of Acoustic Waves
(7.1) Will show that a small (compared to ) source of arbitrary shape and velocity distribution, a
simple source, produces the same field as a small
Lets compare the far-field response with the on axis response. From the near-field on axis response
kr
a 2
p ( r , 0 ) = 2 o cU o sin 1 + 2 1
r
2
The axial pressure amplitude for the far fiel
ECE/TAM 473
Homework Assignment #4
Due: Friday, September 16, 2016
1. Problem 5.2.1a in Kinsler er al.
2. For an acoustic pressure p =105cos [10(600t + 2y) ] Pa, where time is in seconds and y is in m
ECE 473
Homework Assignment #2
Due: Friday, September 2, 2016
1. A mass of 20 kg hanging on a spring is pulled down a distance of 0.1 m and then released. The mass
then oscillates with decreasing ampl
ECE 473
Homework Assignment #2
Due: Friday, September 15, 2017
1. A mass of 10 kg hanging on a spring is pulled down a distance of 0.1 m and then released. The mass
then oscillates with decreasing amp
ECE/TAM 473
Homework Assignment #1
Due: Friday, September 1, 2017
1. Let x e t ( A1 cos t + A2 sin t ) . Show
that x ( t ) Ae t cos (t + ) . Evaluate the constants A and
=
=
in terms of A1 and A2 , t
Chapte 1 - Fund
er
damentals of Vibration
s
(1.2) Simp Harmonic Oscillator (SHO): A simple mode for all wav phenomen
ple
cs
r
s
el
ve
na.
If we unde
erstand the SHO, then we will be abl to quickly und
Cha
apter 2 The Vibrat
T
ting String
g
(2.1) For simple harmo oscillator (one mass the goal w to find t single fun
s
onic
s),
was
the
nction x(t) th
hat
would desc
cribe the ent history of the motion
Nonlinear Acoustic Propagation
In the previous derivation of the acoustic wave equation we considered only linear disturbances. Lets
look briefly at what happens when you include nonlinear terms.
In t
Chapter 9 Cavities and Waveguides
(9.2) Rectangular Cavity
Consider a rectangular cavity
z
Lz
y
Ly
Lx
x
This cavity (or room) has perfectly smooth, rigid walls. This box could approximate a living roo
ECE 473
Homework Assignment #9
Due: Friday, October 28, 2016
1. A pulsating sphere of radius a = 0.15 m radiates spherical waves into air at a frequency of
100 Hz. (a) If the intensity at a distance o
ECE 473
Homework Assignment #7
Due: Friday, October 14, 2016
1. a) A 20 kHz SONAR source is producing sound underwater (assume a B/A = 5 and 1.1 atm
ambient pressure at the depth of the source at 20C)
1. e
t
( A1 cos t + A2 sin t )
Homework # 1 Solutions
Letting A1 = A cos and A2 = A sin then
e t ( A1 cos t + A2 =
sin t ) e t ( A cos cos t A sin sin t )
1
1
sin t
cos (t ) + cos (t + ) and sin =
cfw
Homework # 4 Solutions
P
= for the adiabatic case and relating to the condensation gives
1. Starting with
P0 0
P
= (1 + s ) . Expanding in a series and keeping only the linear terms in s assuming s
Homework # 5 Solutions
1.
a) M av = 44 ( 0.3) + 28 ( 0.3) + 32 ( 0.4 ) = 34.4
=
c
b) =
o
c) =
e
(1.35) (8314 J/kg o K )( 263.16o K )
g RTo
=
M av
34.4
= 293 m/s
g Po
=
c2
(1.35)( 400 Pa
)
=
2
( 293 m/
ECE 473
Homework Assignment #6
Due: Friday, September 30, 2016
1. Kinsler et al. 5.11.2
kr
e j ro c cos e j
=
Sol: z r=
oc
2
1 + (kr )
for cos =
kr
1 + (kr ) 2
k = (2/343)f
kr = 0.00183 f
roc = 415 ra
Homework # 2 Solutions
1.
m = 20 kg
x0 = 0.1 m
= 1/ = 0. 333 s
= 3 s-1
Rm = 2 m = 2 (20) (3) = 120 N.s/m
=
0
s
=
m
200
=
20
d=
02 2=
3.16 rad/s
10 9=
1 rad/s
x = A e cos (dt + ) = A e-3t cos (t + )
ECE/TAM 473
Homework Assignment #4
Due: Friday, September 16, 2016
1. Problem 5.2.1a in Kinsler er al.
2. For an acoustic pressure p =105cos [10(600t + 2y) ] Pa, where time is in seconds and y is in m
ECE 473
Homework Assignment #2
Due: Friday, September 2, 2016
1. A mass of 20 kg hanging on a spring is pulled down a distance of 0.1 m and then released. The mass
then oscillates with decreasing ampl
(5.10) Specific Acoustic Impedance
Specific acoustic impedance
z
p Pa s
or ray1
u m
For plane waves
z 0 c for going waves
The product 0c is the characteristic impedance. It is specified by the pro
Chapter 5 The Acoustic Wave Equation and Simple Solutions
(5.1) In this chapter we are going to develop a simple linear wave equation for sound propagation in
fluids (1D). In reality the acoustic wave
(5.7) Harmonic Plane Waves
The classical wave equation is of the form:
r
2 p% ( r , t )
r
= c 2 2 p% ( r , t )
2
t
r
where r = rx x + ry y + rz z is the position vector.
If we assume that the solutio
Cha
apter 2 The
T Vibratting Stringg
(2.1) For simple
s
harmo
onic oscillator (one masss), the goal w
was to find tthe single funnction x(t) thhat
would desccribe the enttire history of
o the motion
n
(Appendix 1) Solids
We will divide our discussion of waves in solids into two different conditions: (1) bulk propagation,
(2) bar propagation. Each of these will be considered in order below.
(1) Prop