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8/11/2019 Lecture 0 Post

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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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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


0

R id Fi Cli k Q i !


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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


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



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(c) Read angular frequency, , from the wave function:

(d) Compute period, T, from angular frequency,

:

s3.6rad/s0.122

T


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


Hz16.0s3.6

11

Tf


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(g) Draw at t=0:

xxy )rad/cm5.1(sin)cm0.2()0,( y [cm]



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(g) Draw at x=0:

tty )rad/s0.1(sin)cm0.2(),0(


y [cm]

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