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Learning Resources
Web:
Youll be using D2LGuelph homepage:
www.uoguelph.ca
Go to courselink!
LoginSelect 1070
What super fun stuff
do you get access to?
Course info
Access to pretestsTutorials
Sample quizzes and exams
Text: sections 1.2, 1.3, 1.4
Handbook: Study Guide1
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students need to register theirbarcodes on Courselink and sign
up for lab within the first twoweeks of the semester!
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Course Evaluation
50% of your mark comes from 5 quizzes (10% each)
Before writing a quiz: (*course outline pg. 2-3)
Complete lab(s)*
Complete study guide(s)*
Complete online pretest (60%, no attempt limit)
3 attempts for each quiz
8/10or better on ANY attempt gives full 10% for
that quiz
4-7.5gives 2% for EACH attempt
50% of your mark comes from the final exam 3
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Labs
There are 5 labs to be completed (one is online)
Book other four labs through courselink
You should book ALL OF YOUR LABSwithin the first two weeks of the semester!
Before doing a lab: Read the lab outline (found in back of study guide)
Consult textbook for understanding
Compose questions to ask of TA during the lab 4
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Labs Doing the lab:
You have 90 minutes to complete the lab Completed labs will be signed/stamped by TA; this is
brought to quizroom in order to be allowed to write
If you cannot finish in time, you must sign up fornew timeslot and redo the lab!
You must be registered for a lab in order to
participate
no walk-ins allowed (TAs WILL TURNYOU AWAY)
You must be in the lab within the first 15 minutes of
your timeslot (TAs WILL TURN YOU AWAY) 5
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Marks and Conflicts
Marks
YOU are responsible for checking your quiz
marks posted onlinecheck regularly; check
after writing your quiz
For any discrepancies, please contact Cindy Wells
in the quizroom ([email protected])
Final Exam Conflicts
If you have any conflict with the 1070 final exam
(Wed. Dec. 3, 7-9 pm) contact Orbax ASAP!!6
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For 1stquiz, you should know:
SG 1 (waves) & SG2 (acoustics)
which includes.
How to evaluate sin(x), cos(x),
sin-1(x), cos-1(x) in degrees and in radians
understand the small angle approximation
Equation for a travelling wave and for a standing wave
the Relations and SI units for
period (T), frequency (f or )
wavelength ()
Acoustic Resonance
Beats
How to use Logarithms
Decibels and Sound Levels
Acoustic Energy, Power and Intensity
Structure and operation of the human ear
You must also complete Pretest #1 on-line!
Final write date: Friday September 26th
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Small Angle Approximation
For < /20 radians (10o):
sin
cos1
tan= sin/cos
MUST BE IN RADIANS !
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Waves and Cyclic (Periodic) Events
Many biological phenomena are cyclic.
Heartbeats
Circadian rhythms,
Estrus cycles
Swimming patterns of one finned
dolphins Many more e.g.s
Such events are best described as waves. Ill explain why later,trust me
Therefore the study of waves is a major component of thisbiophysics course.
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SIMPLE HARMONIC MOTION SHM
Special Case: Mass & Spring
2 orientations pick the simplest!!
m
m
Demo: people
So a wave moves energy and not matter &
particles oscillate as the wave moves forward
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Object experiences a restoring force proportional to its displacement.
We can define the period T, and frequencyfof oscillation.
Period (T): the time taken to complete one full cycle
Units are seconds
Frequency (f ): the number of cycles per second
Units are Hertz = 1/seconds
y
y = 0y = -A y = +A
Simple Harmonic Motion
F= 0
=
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Can mathematically describe the motion with a sine (or cosine)
is called angular frequency
Units are radians/second
It relates back to period and frequency
y
y = 0y = -A y = +A
Simple Harmonic Motion
= sin
=2
=
1
=
2
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A wave is a disturbance that travels outward from its source
What Is a Wave?
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The water moves up and down as the disturbance
moves outward.
The energy is transported outward from thesource.
The matter (water) is not transported.
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Waves in PHYS*1070 (weeks 2-8)Waves
propagation of a disturbance (produced by oscillations/vibrations)
transport energy (NOT matter!) from one region to another Have characteristic properties/structure
Waves can deflect, interfere, diffract
Matter Waves
Study Guide 2 (acoustics, vibrating strings)
Electromagnetic Waves
Study Guides 3, 4
light, x-rays, microwaves, etc.
Quantum Mechanical Waves
Study guides 4-6
Motion of elementary particles/waves
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Clicker Quiz A periodic wave is traveling to the right on a long, stretched rope.
Points A and B are attached to the rope. When the wave moves a little
to the right, how do these two points move?
A. A and B both move right
B. A and B both move left
C. A moves down and B moves up
D. A moves up and B moves down
E. A and B both move up
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Answer
Before After
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Mechanical WavesParticles that make up the medium undergo displacements as the wave
travels through.
Two main types
transverse wavesparticles move perpendicular to wave direction
longitudinal wavesparticles move parallel to wave direction
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Transverse vs. Longitudinal Waves
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Mathematical Description of Waves
The most general mathematical form for the displacement by a
disturbance is given by a wave function :
= ( )
where is called the phase of the wave.
Which of the following are waves? ALL OF THEM
y = x3.0t
y = (x3.0t)2
y = x + 3.0t
y = (2.4x3.7t)3+ 4.5
y = 6.8 sin(x3.0t) + 1.2
y = (4.0x + 3.0t)2+ 3.0
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Clicker Quiz Which of the following is NOT a wave?
A. y = x + 6.0t
B. y = (3.4x3.0t)3
C. y = (x7.0t2) **
D. y = cos(x4.2t)
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The speed of wave, such as a sound wave, can be found by
measuring the speed of a fixed point in the wave pattern:
Speed of a Wave
),( 1txy
),( 2txy
x
t
xv
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Clicker Quiz
What is the speed of this wave?
x (m)
y (m)
0
3
3 6 x (m)
y (m)
0
3
3 6
t =1s t =3s
A. 0 m/s
B. 1.0 m/s
C. 2.0 m/s
D. 2.3 m/s
E. 4.5 m/s
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Answer
x (m)
y (m)
0
3
3 6 x (m)
y (m)
0
3
3 6
t =1s t =3s
12
12
tt
xx
c
1s3s
m2.5-m7
s2
m4.5
m/s3.2
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Periodic Waves
Periodic wavesare waves whose pattern repeats indefinitely along thedirection of propagation with a fixed period of repetition:
They are produced by sources which vibrate in a periodic way
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y (x,t)
y (x,t)
y (x,t)
Not Periodic
x
x
x
y (x,t)
x
y (x,t)
x xy (x,t)
Periodic
A f i di
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Anatomy of a Periodic Wave
Amplitude, A:
the maximum
displacement ofa particle in the
wave from its
equilibrium
position
crests:the peaks of the wave
troughs:the
lowest points of
the wave
wavelength, : the
distance between two
successive troughs,crests, or any two
points of the same
phase
h i l i i f
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Mathematical Description of Waves
The most general mathematical form for the displacement by a
disturbance is given by a wave function :
Now lets choose a particular shape of wave: sinusoidal (harmonic)
= ( )
= sin( )
W D i i
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Wave Description
)sin(),( tkxAtxy
numberwave2
k [rad/m]
frequencyangular2
2 T
f
[rad/s]
amplitudeA [m]
W S d
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Wave Speed The wave moves forward exactly one wavelength over a time
interval equal to the period . For all waves, we can define a constant
speed of propagation :
=
=
Based on the definitions for and k, another determination for the
wave speed is:
=
=
=
True for both transverse
and longitudinal waves!
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What happens at a fixed position (x)? Note that the wave is sinusoidal in both time, t, and space, x:
a particle at fixed x(e.g. x=0) moves up anddown as a sinusoidal function of time:
)sin(),0( tAty
x=0
Wh t h t fi d ti (t)?
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What happens at a fixed time (t)? Note that the wave is sinusoidal in both time, t, and space, x:
at fixed time(e.g. t=0), the shape of the wave is a sine curve in
space:
)sin()0,( kxAxy
x
y
t = 0
V i bl L d f Si id l W
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Variable Legend for Sinusoidal Waves
amplitude (units depend on type ofwave)
frequency (Hz or cycles/second)
angular frequency (radians/second)
period (seconds)
=
wavelength (metres)
wave speed of propagation
= wave number (radians/metre)
=
, = sin
: wave travelling in +x-direction
+ : wave travelling in -x-direction
Direction of propagation:
R id Fi Cli k Q i !
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Rapid-Fire Clicker Quiz!
What is the amplitudeof this wave?
x (m)
y (m)
0
3
3 6
-3
A: 3 m B: 6 m C: 1.5 m D: 4 m
E: Need more information
R id Fi Cli k Q i !
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Rapid-Fire Clicker Quiz!
What is the wavelengthof this wave?
x (m)
y (m)
0
3
3 6
-3
A: 3 m B: 6 m C: 1.5 m D: 4 m
E: Need more information
0
R id Fi Cli k Q i !
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Rapid-Fire Clicker Quiz!
What is the periodof this wave?
x (m)
y (m)
0
3
3 6
-3
A: 3 m B: 6 m C: 1.5 m D: 4 m
E: Need more information
0
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ExampleA wave traveling along the x-axis is given as:
Where the displacement, y, is in cm.
Determine:
a) the amplitude
b) the wavelength
c) the angular frequency
d) the periode) the frequency
f) the wave speed
g) draw and
xttxy )rad/cm5.1()rad/s0.1(sin)cm0.2(),(
)0,( txy ),0( txy
S l ti
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Solution
(a) Read amplitude from the wave function:
)sin(),( kxtAtxy
cm0.2A(b) Wave function gives wave number, k, which
gives wavelength, :
1cm5.1 k cm2.4cm5.1
221
k
xttxy )rad/cm5.1()rad/s0.1(sin)cm0.2(),(
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(c) Read angular frequency, , from the wave function:
(d) Compute period, T, from angular frequency,
:
s3.6rad/s0.122
T
xttxy )rad/cm5.1()rad/s0.1(sin)cm0.2(),(
srad/0.1
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(e) Compute frequency, f, from period, T:
(f) Compute speed, v, from wavelength, , and
frequency, f:
fv
cm/s67.0
m/s107.6
)Hz16.0()m042.0(
3
xttxy )rad/cm5.1()rad/s0.1(sin)cm0.2(),(
Hz16.0s3.6
11
Tf
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(g) Draw at t=0:
xxy )rad/cm5.1(sin)cm0.2()0,( y [cm]
xttxy )rad/cm5.1()rad/s0.1(sin)cm0.2(),(
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(g) Draw at x=0:
tty )rad/s0.1(sin)cm0.2(),0(
xttxy )rad/cm5.1()rad/s0.1(sin)cm0.2(),(
y [cm]