普通物理－Lecture9－Oscillations & Wavews

(1)

普通物理

Lecture 9

Oscillations & Waves

振盪與波動振盪與波動

(2)



’’



Hooke’s Law

虎克定律虎克定律



Simple Harmonic Motion

簡諧運動簡諧運動



Simple Harmonic Motion and Uniform Circular

Motion

簡諧運動與等速圓周運動簡諧運動與等速圓周運動



Motion as a Function of Time

運動的時間函數運動的時間函數

Motion

簡諧運動與等速圓周運動簡諧運動與等速圓周運動



Motion of a Pendulum

擺錘運動擺錘運動



Damped Oscillations

阻尼振盪阻尼振盪



Damped Oscillations

阻尼振盪阻尼振盪



Wave Motion

波動波動



(3)

Hooke’s Law

虎克定律



 FF_ss = = -- k xk x

–– FF_ss is the spring forceis the spring force

–– k is the spring constantk is the spring constant

 It is a measure of the stiffness of the springIt is a measure of the stiffness of the spring

A

A large klarge k indicates aindicates a stiff springstiff spring and aand a small ksmall k indicates aindicates a softsoft

–– A A large klarge k indicates a indicates a stiff springstiff spring and a and a small ksmall k indicates a indicates a soft soft spring

spring

–– x is the displacement of the object from its x is the displacement of the object from its ilib i iti

ilib i iti equilibrium position equilibrium position

 x = 0 at the equilibrium positionx = 0 at the equilibrium position

–– The negative sign indicates that the force is alwaysThe negative sign indicates that the force is alwaysThe negative sign indicates that the force is always The negative sign indicates that the force is always directed

directed opposite toopposite to the displacementthe displacement

(4)

Hooke’s Law

虎克定律

Hooke’s Law Force



 The force always acts toward the equilibriumThe force always acts toward the equilibrium 

 The force always acts toward the equilibrium The force always acts toward the equilibrium

position position

It i ll d th

It i ll d th t it i ff

–– It is called the It is called the restoring forcerestoring force



 The direction of the restoring force is such that The direction of the restoring force is such that

the object is being either pushed or pulled the object is being either pushed or pulled toward the equilibrium position

(5)

Hooke’s Law

虎克定律

Spring – Mass System Sp g ss Sys e



 When x is positive (to theWhen x is positive (to the 

 When x is positive (to the When x is positive (to the

right), F is negative (to the right), F is negative (to the left)

left) left) left)



 When x = 0 (at equilibrium), When x = 0 (at equilibrium),

F i 0 F i 0 F is 0 F is 0



 When x is negative (to the When x is negative (to the

left), F is positive (to the right) left), F is positive (to the right)

(6)

Hooke’s Law

虎克定律



 Assume the object is initially pulled Assume the object is initially pulled

to a distance

to a distance dd and released fromand released from to a distance

to a distance dd and released from and released from rest

rest



 As the object moves toward theAs the object moves toward the 

 As the object moves toward the As the object moves toward the

equilibrium position,

equilibrium position, FF and and aa

decrease but

decrease but vv increasesincreases decrease, but

decrease, but vv increasesincreases



(7)

Hooke’s Law

虎克定律



 The The FF andand a a start to increase in the opposite start to increase in the opposite

direction and

direction and vv decreasesdecreases direction and

direction and vv decreasesdecreases



 The motion momentarily comes to a stop at The motion momentarily comes to a stop at x = x = -- dd 

 It then accelerates back toward the equilibrium It then accelerates back toward the equilibrium

position position



 The motion continues indefinitelyThe motion continues indefinitely

(8)

Example 1

A spring is hung vertically, and an object of mass m is attached to the lower end of the spring and slowly lowered a distance d to the equilibrium point. Find the value of the p g y q p spring constant if the spring is displaced by 2.00 cm and the mass is 0.550 kg.

(9)

Simple Harmonic

Simple Harmonic Motion

Motion

簡諧運動



Motion that occurs when the net force

along the direction of motion obeys

Hooke’s Law

–– The force is proportional to the displacement and The force is proportional to the displacement and always directed toward the equilibrium position always directed toward the equilibrium position



The motion of a spring mass system is an

example of Simple Harmonic Motion

p



Not all periodic motion over the same

path can be considered Simple Harmonic

motion

99



To be Simple Harmonic motion,

the force

needs to obey Hooke’s Law

(10)

Simple Harmonic

Simple Harmonic Motion

Motion

簡諧運動

Amplitude p ude 振幅振幅 



Amplitude, A

p

–– The amplitude is the The amplitude is the maximum positionmaximum position of of the object relative to the equilibrium

the object relative to the equilibrium the object relative to the equilibrium the object relative to the equilibrium position

position In the

In the absence of frictionabsence of friction an object in simplean object in simple

–– In the In the absence of frictionabsence of friction, an object in simple , an object in simple harmonic motion will oscillate between the harmonic motion will oscillate between the positions

positions x =x = ±±AA

positions

(11)

Simple Harmonic

Simple Harmonic Motion

Motion

簡諧運動

Period and Frequency 週期與頻率



 The period,The period, TT, is the time that it takes for the, is the time that it takes for the 

 The period, The period, TT, is the time that it takes for the , is the time that it takes for the

object to complete one complete cycle of motion object to complete one complete cycle of motion

–– From x = A to x =From x = A to x = -- A and back to x = AFrom x A to x From x A to x A and back to x AA and back to x = AA and back to x A



 The frequency, The frequency, ƒƒ, is the number of complete , is the number of complete

cycles or vibrations per unit time cycles or vibrations per unit time cycles or vibrations per unit time cycles or vibrations per unit time

–– ƒ = 1 / Tƒ = 1 / T

F i th i l f th i d F i th i l f th i d

–– Frequency is the reciprocal of the periodFrequency is the reciprocal of the period

11 11

(12)

Simple Harmonic

Simple Harmonic Motion

Motion

簡諧運動

Acceleration of an Object in Simple Harmonic Motion Acceleration of an Object in Simple Harmonic Motion



 Newton’s second law will relate force and Newton’s second law will relate force and

acceleration acceleration



 The force is given by Hooke’s LawThe force is given by Hooke’s Law 

 The force is given by Hooke s LawThe force is given by Hooke s Law 

 F = F = -- k x = m ak x = m a

aa kx / mkx / m –– a = a = --kx / mkx / m



(13)

Example 2

A 0.350-kg object attached to a spring of force constant 1.30×102 _{N/m is free to move}

on a frictionless horizontal surface. If the object is released from rest at x=0.100 m, find j , the force on it and its acceleration at x=0.100 m, x=0.050 m, x=0 m, and x=-0.100 m.

13 13

(14)

Simple Harmonic

Simple Harmonic Motion

Motion

簡諧運動

Elastic Potential Energy Elastic Potential Energy



A compressed spring has

potential energy

–– The compressed spring, when allowed to The compressed spring, when allowed to

expand can apply a force to an object expand can apply a force to an object expand, can apply a force to an object expand, can apply a force to an object

–– The potential energy of the spring can be The potential energy of the spring can be

t f d i t

t f d i t ki tiki ti f thf th bj tbj t

transformed into

(15)

Simple Harmonic

Simple Harmonic Motion

Motion

簡諧運動



 The energy stored in a stretched or compressed The energy stored in a stretched or compressed

spring or other elastic material is called elastic spring or other elastic material is called elastic potential energy potential energy 2

1

₂

2

1 kx

PE

_s





 The energy is stored only when the spring is The energy is stored only when the spring is

stretched or compressed stretched or compressed



 Elastic potential energy can be added to the Elastic potential energy can be added to the

15 15

statements of

statements of Conservation of Energy and Conservation of Energy and Work

(16)

Simple Harmonic

Simple Harmonic Motion

Motion

簡諧運動

Energy in a Spring Mass System



 A block sliding on aA block sliding on a

e gy Sp g ss Sys e



 A block sliding on a A block sliding on a

frictionless system collides frictionless system collides with a light spring

with a light spring with a light spring with a light spring



 The block attaches to the The block attaches to the

spring spring spring spring



 The system oscillates in The system oscillates in

Simple Harmonic Motion Simple Harmonic Motion Simple Harmonic Motion Simple Harmonic Motion

(17)

Simple Harmonic

Simple Harmonic Motion

Motion

簡諧運動

Energy Transformationse gy s o o s



 The block is moving on a frictionless surfaceThe block is moving on a frictionless surface 

 The total mechanical energy of the system is The total mechanical energy of the system is

the kinetic energy of the block the kinetic energy of the block the kinetic energy of the block the kinetic energy of the block

17 17

(18)

Simple Harmonic

Simple Harmonic Motion

Motion

簡諧運動

Energy Transformations



 The spring is partially compressedThe spring is partially compressed

e gy s o o s



 The energy is shared between kinetic energy The energy is shared between kinetic energy

and elastic potential energy and elastic potential energy



 The total mechanical energy is the sum of the The total mechanical energy is the sum of the

kinetic energy and the elastic potential energy kinetic energy and the elastic potential energy

(19)

Simple Harmonic

Simple Harmonic Motion

Motion

簡諧運動



 The spring is now fully compressedThe spring is now fully compressed



 The block momentarily stopsThe block momentarily stops 

 The total mechanical energy is stored as elastic The total mechanical energy is stored as elastic gygy

potential energy of the spring potential energy of the spring

19 19

(20)

Simple Harmonic

Simple Harmonic Motion

Motion

簡諧運動



 When the block leaves the spring, the total When the block leaves the spring, the total

p g,

mechanical energy is in the kinetic energy of mechanical energy is in the kinetic energy of the block

the block



 The spring force is conservative and the total The spring force is conservative and the total

energy of the system remains constant energy of the system remains constant

(21)

Simple Harmonic

Simple Harmonic Motion

Motion

簡諧運動

Velocity as a Function of Position



 Conservation of Energy allows a calculation of Conservation of Energy allows a calculation of

the velocity of the object at any position in its the velocity of the object at any position in its

Ve oc y s u c o o os o

the velocity of the object at any position in its the velocity of the object at any position in its motion motion k

_

₂ ₂

_

k v A x m   

–– Speed is a maximum at Speed is a maximum at x = 0x = 0 –– Speed is zero at Speed is zero at x = x = ±±AA

–– The The ±± indicates the object can be traveling in either indicates the object can be traveling in either direction

direction

21 21

(22)

Example 3

A 0.500-kg object connected to a light spring with a spring constant of 20.0 N/m oscillates on a f i i l h i l f ( ) l l h l f h d h i

frictionless horizontal surface. (a) calculate the total energy of the system and the maximum speed of the object if the amplitude of the motion is 3.00 cm. (b) What is the velocity of the object when the displacement is 2.00 cm? (c) Compute the kinetic and potential energies of the

t h th di l t i 2 00 system when the displacement is 2.00 cm.

(23)

Simple Harmonic Motion and

Uniform Circular Motion



 A ball is attached to the rim A ball is attached to the rim

of a turntable of radius A of a turntable of radius A



 The focus is on the shadow The focus is on the shadow

that the ball casts on the that the ball casts on the screen

screen



 When the turntable rotates When the turntable rotates

ith t t l

with a constant angular with a constant angular

speed, the shadow moves in speed, the shadow moves in

simple harmonic motion simple harmonic motion simple harmonic motion simple harmonic motion

23 23

(24)

Simple Harmonic Motion and

Uniform Circular Motion

Period and Frequencye od d eque cy



 PeriodPeriod _T  ₂ m

–– This gives the time required for an object of mass m This gives the time required for an object of mass m

k

g q j

attached to a spring of constant k to complete one attached to a spring of constant k to complete one cycle of its motion

cycle of its motion



(25)

Simple Harmonic Motion and

Uniform Circular Motion

Angular Frequency



 The angular frequency is related to the frequencyThe angular frequency is related to the frequency

k

ƒ

2 







 TheThe frequencyfrequency gives the number of cycles pergives the number of cycles per

m

ƒ

2





 The The frequencyfrequency gives the number of cycles per gives the number of cycles per

second second



 TheThe angular frequencyangular frequency gives the number ofgives the number of



 The The angular frequencyangular frequency gives the number of gives the number of

radians per second radians per second

25 25

(26)

Example 4

A 1.30 x 103_{-kg car is constructed on a frame supported by four springs. Each spring has a spring}

f 2 00 104 _N/ _If _{l idi} _{i h} _h _{bi d} _{f 1 60 10}2 _k

constant of 2.00 x 104 _{N/m. If two people riding in the car have a combined mass of 1.60 x 10}2 _kg,

find the frequency of vibration of the car when it is driven over a pothole in the road. Find also the period and the angular frequency. Assume the weight is evenly distributed.

(27)

Motion as a Function of Time



 Use of a Use of a _{reference circle}_{reference circle}

allows a description of the allows a description of the motion

motion



 x = A cos (2x = A cos (2ƒt)ƒt)ƒƒ

–– x is the position at time tx is the position at time t

–– x varies between +A and x varies between +A and --A

A

27 27

(28)

Motion as a Function of Time

Graphical Representation of Motion

)

2 cos(

)

cos(

t

A

ft

A

x











 When x is a maximum or When x is a maximum or

i i l it i i i l it i

)

(

)

(

f

minimum, velocity is zero minimum, velocity is zero



 When x is zero, the When x is zero, the

velocity is a maximum velocity is a maximum



(29)

Motion as a Function of Time

Motion Equationso o qu o s



Remember the uniformly accelerated motion



Remember, the uniformly accelerated motion

equations cannot be used



x = A cos (2

ƒt) = A cos

ƒt) = A cos



tt



v = --22ƒA sin (2

v =

v

v 22ƒA sin (2

ƒA sin (2ƒt) =

ƒA sin (2ƒt)

ƒt) = --A

ƒt) A

A

A 

 sin



 sin

sin

sin 



tt



a =

a = --44



22

ƒƒ

22

A cos (2

ƒt) =

ƒt) = --A

A



22

cos



tt

29 29

(30)

Motion as a Function of Time

Verification of Sinusoidal Nature Ve c o o S uso d N u e



 This experiment showsThis experiment shows 

 This experiment shows This experiment shows

the sinusoidal nature of the sinusoidal nature of simple harmonic motion simple harmonic motion simple harmonic motion simple harmonic motion



 The spring mass system The spring mass system

oscillates in simple oscillates in simple oscillates in simple oscillates in simple harmonic motion harmonic motion 

 The attached pen tracesThe attached pen traces 

(31)

Example 5

(a)Find the amplitude, frequency, and period of motion for an object vibrating at the end of a h i l i if h i f i i i f i f i i (0 250 ) ( /8) (b) horizontal spring if the equation for its position as a function of time is x=(0.250 m) cos (πt/8) (b) Find the maximum magnitude of the velocity and acceleration. (c) What is the position, velocity, and acceleration of the object after 1.00 s has elapsed ?

(a)

(b) (b)

31 31

(32)

Example 5

(a)Find the amplitude, frequency, and period of motion for an object vibrating at the end of a

h i l i if h i f i i i f i f i i X (0 250 ) ( /8) (b) horizontal spring if the equation for its position as a function of time is X=(0.250 m) cos (πt/8) (b) Find the maximum magnitude of the velocity and acceleration. (c) What is the position, velocity, and acceleration of the object after 1.00 s has elapsed ?

(33)

Motion of a

Pendulum



 The simple pendulum is The simple pendulum is

another example of another example of

i l h i ti

simple harmonic motion simple harmonic motion



 The force is the The force is the

t f th i ht

component of the weight component of the weight tangent to the path of

tangent to the path of motion motion motion motion F F ii θθ –– FF_tt = = -- m g sin m g sin θθ 33 33

(34)

Motion of a

Pendulum



 In general, the motion of a pendulum is not In general, the motion of a pendulum is not

simple harmonic simple harmonic simple harmonic simple harmonic



 However, for small angles, it becomes simple However, for small angles, it becomes simple

harmonic harmonic harmonic harmonic

–– In general, angles < 15In general, angles < 15°° are small enoughare small enough

ii θ θθ θ

–– sin sin θ = θθ = θ

(35)

Motion of a

Pendulum

Period of Simple Pendulum Period of Simple Pendulum

L

2 T







This shows that the period is independent

g

2 T







This shows that the period is independent

of the amplitude



Th

i d

d

th

l

th

f th



The

period

depends on the

length

of the

pendulum and the

acceleration of gravity

t th l

ti

f th

d l

t th l

ti

f th

d l

at the location of the pendulum

35 35

(36)

Example 6

Using a small pendulum of length 0.171 m, a geophysicist counts 72.0 complete swings in a time of 60 0 s What is the value of g in this location?

(37)

Motion of a

Pendulum

Simple Pendulum Compared to a Spring-Mass System Simple Pendulum Compared to a Spring-Mass System

37 37

(38)

Motion of a

Pendulum

Physical Pendulumys c e du u



 A physical pendulumA physical pendulum 

 A physical pendulum A physical pendulum

can be made from an can be made from an object of any shape object of any shape object of any shape object of any shape



 The center of mass The center of mass

oscillates along a oscillates along a oscillates along a oscillates along a circular arc circular arc

(39)

Motion of a

Pendulum

Period of a Physical Pendulum



 The period of a physical pendulum is given byThe period of a physical pendulum is given bypp p yp y pp gg yy

2 I

T





I is the object’s moment of inertia I is the object’s moment of inertia

2 T

mgL





–– I is the object s moment of inertiaI is the object s moment of inertia

–– m is the object’s massm is the object’s mass



 For a simple pendulum I = mLFor a simple pendulum I = mL22 and theand the 

 For a simple pendulum, I = mLFor a simple pendulum, I = mL and the and the

equation becomes that of the simple pendulum equation becomes that of the simple pendulum as seen before as seen before 39 39 as seen before as seen before

(40)

Damped Oscillations

阻尼振盪



Only ideal systems oscillate indefinitely



In real systems,

friction

retards the

motion



Friction reduces the

total energy of the

system

and the oscillation is said to be

system

and the oscillation is said to be

damped

(41)

Damped Oscillations

阻尼振盪



 DD dd titi ii 

 Damped motion varies Damped motion varies

depending on the fluid used depending on the fluid used With a low viscosity fluid With a low viscosity fluid

–– With a low viscosity fluid, With a low viscosity fluid, the vibrating motion is the vibrating motion is

preserved, but the amplitude preserved, but the amplitude

p , p

of vibration decreases in of vibration decreases in time and the motion

time and the motion ultimately ceases

ultimately ceases

 This is known as This is known as

d d d

d d d ill tiill ti 次次

underdamped

underdamped oscillationoscillation次次阻尼振盪

阻尼振盪

41 41

(42)

Damped Oscillations

阻尼振盪



 With a higher viscosity, the object returns With a higher viscosity, the object returns

rapidly to equilibrium after it is released and rapidly to equilibrium after it is released and p d y o equ b up d y o equ b u ee s e e seds e e sed dd does not oscillate

does not oscillate

The s stem is said to be

The s stem is said to be itiiti ll dll d dd 臨界阻尼臨界阻尼 –– The system is said to be The system is said to be critically damped critically damped 臨界阻尼臨界阻尼



 With an even higher viscosity, the piston With an even higher viscosity, the piston

ilib i i h i h h

returns to equilibrium without passing through returns to equilibrium without passing through the equilibrium position, but the time required the equilibrium position, but the time required

(43)

Damped Oscillations

阻尼振盪

Graphs of Damped Oscillators G p s o ped Osc o s



 Plot Plot aa shows an shows an

underdamped oscillator underdamped oscillator



 PlotPlot bb shows a criticallyshows a critically 

 Plot Plot bb shows a critically shows a critically

damped oscillator damped oscillator



 PlotPlot cc shows anshows an 

 Plot Plot cc shows an shows an

overdamped oscillator overdamped oscillator

43 43

(44)

Wave Motion

波動



 A wave is the motion of a disturbanceA wave is the motion of a disturbance 

 Mechanical waves requireMechanical waves requireqq

–– Some source of disturbanceSome source of disturbance

–– A medium that can be disturbedA medium that can be disturbed

–– Some physical connection between or mechanism Some physical connection between or mechanism through which adjacent portions of the medium through which adjacent portions of the medium influence each other

influence each other



(45)

Wave Motion

波動

Types of Waves – Traveling Waves 行進波



 Flip one end of a long Flip one end of a long

th t i d

rope that is under rope that is under

tension and fixed at one tension and fixed at one end

end end end



 The pulse travels to the The pulse travels to the

right with a definite right with a definite right with a definite right with a definite speed

speed



 A disturbance of thisA disturbance of this 

 A disturbance of this A disturbance of this

type is called a

type is called a traveling traveling wave wave 45 45 wave wave

(46)

Wave Motion

波動

Types of Waves – Transverseypes o W ves sve se橫波橫波



 In a transverse wave, each element that is In a transverse wave, each element that is

disturbed moves in a direction perpendicular to disturbed moves in a direction perpendicular to the wave motion

(47)

Wave Motion

波動

Types of Waves – Longitudinal ypes o W ves o g ud 縱波縱波



 In a longitudinal wave, the elements of the In a longitudinal wave, the elements of the gg ,,

medium undergo displacements parallel to the medium undergo displacements parallel to the motion of the wave

motion of the wave



 A longitudinal wave is also called a A longitudinal wave is also called a

compression wave compression wave 壓縮波壓縮波 compression wave compression wave 壓縮波壓縮波 47 47 

 Waves may be a combination of transverse and Waves may be a combination of transverse and

longitudinal longitudinal

(48)

Wave Motion

波動

Waveform 波形– A Picture of a Wave

W ve o 波形 c u e o W ve



 The brown curve is aThe brown curve is a 

 The brown curve is a The brown curve is a

“snapshot” of the wave at “snapshot” of the wave at some instant in time

some instant in time some instant in time some instant in time



 The blue curve is later in The blue curve is later in

ti ti

time time



(49)

Wave Motion

波動

Longitudinal Wave Represented as a Sine Curve



 A longitudinal wave can also be represented as A longitudinal wave can also be represented as

a sine curve a sine curve



 Compressions correspond to crests and Compressions correspond to crests and

stretches correspond to troughs stretches correspond to troughspp gg



 Also called density waves or pressure wavesAlso called density waves or pressure waves

49 49

(50)

Description of a Wave

波的描述



 A steady stream of A steady stream of

pulses on a very long pulses on a very long

p y g p y g string produces a string produces a continuous wave continuous wave 

 The blade oscillates in The blade oscillates in

simple harmonic motion simple harmonic motion



 Each small segment of Each small segment of

the string, such as P, the string, such as P,

(51)

Description of a Wave

波的描述

Amplitude and Wavelengthp ude d W ve e g



 Amplitude, Amplitude, AA , is the , is the

maximum displacement maximum displacement of string above the

of string above the equilibrium position equilibrium position



 Wavelength, Wavelength, g ,g , ,,λλ, is the , is the

distance between two distance between two successive points that successive points that pp behave identically

behave identically

51 51

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Description of a Wave

波的描述

Speed of a Wave  

v =

v = λλ/ T = ƒ

/ T = ƒ λλ

 

v =

v = λλ/ T = ƒ

/ T = ƒ λλ

–– Is derived from the basic speed equation of Is derived from the basic speed equation of distance/time

distance/time



This is a general equation that can be

g

q

applied to many types of waves

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Example 7

A wave traveling in the positive x-direction is pictured in figure below. Find the amplitude wavelength speed and period of the wave if it has a frequency of 8 00 amplitude, wavelength, speed and period of the wave if it has a frequency of 8.00 Hz. In the figure, Δx=40.0 cm and Δy=15.0 cm.

53 53

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Description of a Wave

波的描述

Speed of a Wave on a String Speed o W ve o S g



The speed of a wave on a string stretched

d

t

i

F

d

t

i

F

under some tension, F

F m

v  where  

 is called the linear densityis called the linear density線密度線密度

v where

L

 

 

 is called the linear densityis called the linear density線密度線密度 

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Example 8

55 55

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Interference of Waves

波的干涉波的干涉



 Two traveling waves can meet and pass Two traveling waves can meet and pass

through each other without being destroyed or through each other without being destroyed or

lt d

even altered even altered



 Waves obey the Waves obey the _{Superposition Principle}_{Superposition Principle}重疊原理重疊原理 –– If two or more traveling waves are moving through If two or more traveling waves are moving through

a medium, the resulting wave is found by adding a medium, the resulting wave is found by adding together the displacements of the individual waves together the displacements of the individual waves together the displacements of the individual waves together the displacements of the individual waves point by point

point by point

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Interference of Waves

Constructive Interference相長性干涉

Co s uc ve e e e ce相長性干涉



 Two waves, Two waves, aa and and bb, ,

have the same have the same have the same have the same frequency and frequency and amplitude amplitude amplitude amplitude

–– Are Are in phasein phase



 The combined waveThe combined wave 

 The combined wave, The combined wave,

cc, has the same , has the same frequency and a frequency and a qq yy greater amplitude greater amplitude 57 57

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Interference of Waves

Constructive Interference in a String Co s uc ve e e e ce S g



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Interference of Waves

Destructive Interference相消性干涉



 Two waves, Two waves, aa and and bb, ,

have the same have the same amplitude and amplitude and frequency

frequency



 They are They are yy 180180°° out of out of

phase phase



 When they combine,When they combine, 

 When they combine, When they combine,

the waveforms cancel the waveforms cancel

59 59

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Interference of Waves

Destructive Interference in a String



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Reflection of Waves

波的反射波的反射

Fixed End Fixed End



 Whenever a traveling wave Whenever a traveling wave gg

reaches a boundary, some or reaches a boundary, some or all of the wave is reflected

all of the wave is reflected



 When it is reflected from a When it is reflected from a

fixed end, the wave is

fixed end, the wave is invertedinverted



 The shape remains the sameThe shape remains the same

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Reflection of Waves

波的反射波的反射

FreeEnd FreeEnd



 When a traveling wave reaches a boundary, all When a traveling wave reaches a boundary, all gg y,y,

or part of it is reflected or part of it is reflected



 When reflected from a free end, the pulse is When reflected from a free end, the pulse is ,, pp not not

inverted inverted

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Assignment 9

gg

63 63

普通物理－Lecture9－Oscillations & Wavews

普通物理

Lecture 9

Oscillations & Waves

Contents





’’





Hooke’s Law

Hooke’s Law





Simple Harmonic Motion

Simple Harmonic Motion





Simple Harmonic Motion and Uniform Circular

Simple Harmonic Motion and Uniform Circular

Motion

Motion





Motion as a Function of Time

Motion as a Function of Time

Motion

Motion





Motion of a Pendulum

Motion of a Pendulum





Damped Oscillations

Damped Oscillations





Damped Oscillations

Damped Oscillations





Wave Motion

Wave Motion



Hooke’s Law

Hooke’s Law

虎克定律

虎克定律

Hooke’s Law

Hooke’s Law

虎克定律

虎克定律

Hooke’s Law

Hooke’s Law

虎克定律

虎克定律

Hooke’s Law

Hooke’s Law

虎克定律

虎克定律

Hooke’s Law

Hooke’s Law

虎克定律

虎克定律

Simple Harmonic

Simple Harmonic Motion

Motion

簡諧運動

簡諧運動

Motion that occurs when the net force

Motion that occurs when the net force

along the direction of motion obeys

along the direction of motion obeys

Hooke’s Law

Hooke’s Law

The motion of a spring mass system is an

The motion of a spring mass system is an

example of Simple Harmonic Motion

example of Simple Harmonic Motion