I. Vibrations occur in:

1. ______________________________________

2. ______________________________________

3. ______________________________________

4. ______________________________________

5. ______________________________________

6. ______________________________________

7. ______________________________________

8. ______________________________________

In addition, vibrations cause ___________ .

Vibrations can be understood by using

_____________________________ as models.

Vibrations and Waves

Ex 1: Draw the forces that act on the pendulumbob at points A, B and C.

B

AC

At A: At B:

In all 3 cases, Fnet ___________________. This must be

true because ________________________________________

and so it is _______________________ .

w|| is the part of w that is ______________________motion.w|| _______________ as increases

w|| pulls the bob back towards __________________

w|| is called a ___________________ force.

The weight w can be ______________________________ :

w wequilibrium

This componentis ______________to the motion andis ____________ in direction to the____________

Ex 2: Vibrating mass m on a spring with constant k:

mm

equilibrium

spring

Draw the forces that act on the mass at the points shown:

Except at x = 0, Fnet ____________________________

FS _________________ as x increases

FS pulls the mass back towards __________________

FS is also a ______________________ force.

xxcompression stretching

x =0

A. Simple _______________ motion (SHM):

--vibrations in an ______________ material

-- due to a restoring force that is __________

____________________ to a displacement.

F =

= -kx

From Newton's 2nd Law, we know that F = ______

Calculus tells us that a = ___________________________:

The solutions to this equation are _____________________

SHM occurs because of ____________________ :

= -kx

x time

______ curve:

______ curve:

x time

Both of these curves are ______________ and

describe the __________________________ that is

___________________________________________.

T = ________________________

B. period T: the time for ______________________________

SI unit for T: _______________

Ex: It takes a pendulum 40 seconds to complete 10complete back and forth swings (10 cycles). What is its period?

T = =

C. frequency f:

Ex: Find the frequency of vibration for the above example.

f = =

f =

Notice that ______________ is ignored as a unit.

Other ___________ can be used for T and f. But when

the time is in _______________ , the unit for frequency is:

or

This unit is called a _____________

It is _____________ from the fundamental unit ____ .

So the answer to the last example can be written:

Notice: T =

f =

f =

From this example, it can be seen that

period and frequency are _____________ :

D. ______________ objects (including metal, air in a

container, glass, string under tension, wood, etc)

“bounce back” when _______________ , _______________

or ________________ .

They vibrate at a special set of __________________

determined by their:

-size: _________ object ___________ f

-material: __________material ____________ f

-shape

-condition

E. An object’s _____________ frequency is the one that

requires the _____________ energy to begin and continue.

It also results in the _________________________ vibrations.

Ex: What determines the natural frequency ofa simple pendulum?

Ex: What determines the natural frequency ofa mass on a spring?

1. _____________________________ stiffer ____________ _____________ frequency

______________________

_____________________ ____________ frequency

2. _____________________________ more _____________ _____________ frequency

F. _______________ occurs when an object is _____________ ______________ at its _________________ frequency.

During resonance, the ________________ (NOT the ______________ ) of vibration is ______________.

Resonating things include:•_______________________•_______________________•_______________________•_______________________•_______________________•_______________________•_______________________•_______________________•_______________________

__________________ forces applied at the system's

________________frequency can lead to ________________ .

Is the frequency changing?

How can you tell?

A

t

II. Pulses and Waves

medium – what a pulse or wave _________________________

__________ (The plural of medium is __________ .)

Pulses and waves are caused by ____________________

and transmit ____________ (but NOT ____________)

through the __________________ .

_____________ sourcedisturbs themedium here

energy moves

_______________

the source by the

pulse or wave

Medium

Ex. 1: ____________ waves:

– require a medium: _______________________

because the wave ____________________________

of the medium as it passes through it

- ___________ propagate in a vacuum

Ex. 2: ____________ waves:

– ________________________ a medium

- are composed of _______________________ fields

- can propagate ___________________ as well as

in solids, liquids and gases.

Examples of Waves (or Pulses) and their Media:

pulse - a __________________________ that propagates through a medium

v = ______________ of pulse

___________ position of'the particles in medium

amplitude A - _______________________________of the medium as the pulse or wave passes through it

wave - a ___________________________disturbance that propagates through a medium

______________

Only ___________________ is usually shown. Unless

otherwise stated, it is usually assumed that the wave

___________________________________________________

The diagram shows a __________________ at one time.

position of medium

A. The amplitude A of a wave determines how much

_____________ it transmits. The energy transported

is proportional to the ___________________ .

Sound: Amplitude determines ______________

small A: ________ large A: _________

Light: Amplitude determines ________________

small A: ________ large A: _________

Amplitude: _______ _______ ________

Energy: _______ _______ ________

Time

Ex: Radio waves and light are types of ___________________

radiation. One way that information can be sent by

radio waves is by _____________________ (changing) the

wave's ___________________ : This is called _______.

Here is how it is created:

1. This wave has the ___________________

2. This wave is called the ____________

3. This is the ___________The ____________ wave'samplitude has been ______________ by wave 1.

B. 3 basic types of waves (or pulses):

1. _______________ waves:

The medium v is ___ the wave v

Ex: ____________________________ wave v

x equilibrium

_________________ of the medium as the wave moves to the right:

Where is the displacement zero?

_______ v

2. _________________ waves

The medium v is ___ the wave v

Ex: ___________________________ wave v

_________________ of the medium as the wave moves to the right:

Where is the displacement zero?

_______ v

3. ________________ waves:

The medium v is __________________ to the wave v.

Ex: ____________________________________

medium v

wave v

Because it is easier to visualize, both

___________________ and ____________________waves

are drawn as if they were _________________ waves.

Ex. A transverse pulse moving to the right:

particle ____________

later

later

later

later

Note: particle of medium moves _____ to wave v

_________displacement

moving ____

moving __________

____________

Ex. A transverse wave moving to the right:In which direction is the medium moving at points…

1

2

3

4

5

6

Imagine the wave at a slightly later time.

Note: Top points 1 and 5 are moving __________Bottom point 3 is moving _________Points 2 and 6 are moving ___________Point 4 is moving ____________.

Ex. A transverse wave moving to the left:In which direction is the medium moving at points…

1

2

3

4

5

6

Imagine the wave at a slightly later time.

Note: Top points 1 and 5 are moving

___________.Bottom point 3 is moving __________Points 2 and 6 are moving _________Point 4 is moving __________.

C. _______________ (__________): the ______________

between two __________________ points on a wave

that have the same:

1. _____________________________ , and

2. __________________________ .

x

y

z

_____________ same ______________ from equilibrium.

Only __________ moving in the same ________________.

= ____

= ____

In sum, is the distance between consecutive

_________________on a wave.

Wavelengths are sometimes measured in terms of

________________ . In this case:

____ = _________

____ = _________

____ = _________

____ = _________

These angles are sometimes called the ______________

or the ____________________ of the wave.

Two points on a wave that are 1 (3600) apart or

a multiple of 1 are said to be ____________________

Two points on a wave that are (½) (1800) apart or

a multiple of (1/2) are said to be __________________

________________________ .

A

B

Ex. Label points on the wave below that are in phase with point A. Then label the points that are completelyout of phase with A. Repeat for point B. = in phase

= out of phase

D. The Speed of any Wave

The speed v of a wave depends on…

1/ ….what __________________ it travels through.

E.g., air vs. water vs. glass vs. earth vs. etc….

…or the __________ of a medium (a _____________)

2/ ….the ______________________ of that medium.

E.g., temp. vs. pressure vs. "elastic-ness" vs. density

3/ …but NOT on the __________________ of the wave.

Ex. sound

Sound is a ____________________ wave. It is transmitted

by the _____________ of atoms or by the _______________

of particles that are bonded to each other. The atoms

exchange ______ (motion) or ________ (bonding).

atom atom atom atom

atom atom atom atom

collisions (in gases and liquids):

vibrations (in solids):

Sound waves are _______________________ :

in air: __________ m/s at STP

in water: ____________

in steel: ____________

Sound travels ________________ at higher air tempsbecause ______________________________________.

The speed of __________ waves in different media:

Mechanical waves such as sound travel ___________

in _________ media because __________________________

___________________________________________________ .

increasing_________

Unless a wave enters a new _______________ , or the medium _______________ , the wave speed will be _______________ , and its acceleration is __________ .

Ex. light

Light is a _____________________________________ wave.

It requires __________________________.

The speed of __________ waves in different media:

in vacuum: _______________ m/s

This speed is given the symbol ______.

Electromagnetic waves such as light travel __________

___________ in denser media because the light must be

_____________ by one atom and then has to be

_____________ by the same atom before moving

on to the next atom. This process _________________

the overall speed. In between atoms, the light

travels at ______ .

in water: _________________in glass: _________________

in air: _________________increasing_________

= __________

= __________

_________ density more _________ ___________ speed

v =

Ex. Three train cars pass a point in one second.

If each car is 10 m long, how fast is the train moving?

v =

=

Instead of cars, think: waves

123

v =

Finding an Equation for the Speed of a Wave.

Because f = v = f can be written:

v =

Compare this to v =

Conclusion:

One __________________ is the distance that

a wave travels in a time of one __________________ .

Stated another way:

One ______________ is the time it takes a wave to

travel a distance of one ___________________ .

The wave travels this far

in a time ______

wave

Ex: Find the speed of a water wave that has awavelength of 5.5 meters and a frequency of 2.8 Hz.

How long with it take this wave to travel a mile(1610 m)?

Given:

Given:

v =

v =

________ f _______

The speed of sound waves in _____ and of light waves in a__________ (and in air for the most part) is _______________of the frequency. Then v is ___________ , and v = f means:

________ f _______

As long as the speed is ____________,

there is ______________relationship

between the ________________ and

the _______________________ .

f

Sound: Frequency determines ______________

low f: ________ high f: _________

Light: Frequency determines ________________

low f: ________ high f: _________

Wavelength: ___________ ____________

Frequency: ___________ ____________

Sound: ___________ ____________

Light: ___________ ____________

Reference Tables: page _______:

__________ light

only ____________Hz

Visible light is only a _______ fraction of the E&M spectrum.

________frequency

________frequency

________wavelength

________wavelength

Ex: Radio waves and light are types of ___________________

radiation. One way that information can be sent by

radio waves is by _____________________ (changing) the

wave's ___________________ : This is called FM. Here

is how it is done:

1. This wave has the ___________________

2. This wave is calledthe ____________

3. This is the ___________The ____________ wave'sfrequency has been ______________ by wave 1.

Do not confuse radio waves sent as ___________________

waves with sound waves, which are ___________________

waves.antenna or satellitetransmits ________ waves

A radio or computer receives______________ waves. It then converts them into________________ signals, which it sends to a speaker. The speaker turns them into _______________________waves,which you can hear.

antenna

antennaon a radio

________ energy ___________energy ________ energy

Ex. String (or wind) instruments are played by makingthe string (or tube) _____________________________ .

v = f

v is _________________ for a fixed tension.

Shorter string _____________ f ___________

v =

v =

vibrating string f

L = _______

L is ___________ ,so is ____________ .

Now shorten the string or tube:

___________ f

Ex. strings or wires

v ~ T (m/L)

waves travel on the strings

Increasing T or using thinner wires ____________v.

For a fixed string length (a fixed ), if v is _____________ ,

f will ________________.

v = f:

A bug jumps once on a pond,creating a pulse.(top view)

_____________ : all points drawn are the __________ of the pulse all points have ___________________________ the shape is __________________

bug

E. The Doppler Effect

A bug jumps at a ___________,creating waves.

bugside viewof waves

What would a diagram of the troughs look like?

The wave v's are ______________________ to the wavefronts.

Far away from the wave source, the wavefronts become

_________________ and more like _________________.

wavefronts = surfaceswith ____________________

Far away, the wave velocity vectors become ____________

old wavefront is__________________

Now bug moves leftwhile jumping at aconstant frequency

1234

newer wavefront_________________

_________ _________ f

_________ _________ f

It doesn't matter whether the ____________ is moving…

Observer measures:

_________ _________ f

_________ _________ f

…or if the ____________ is moving with the source at rest:

Observer measures:

_________ _________ f

observer: wave source:

_________ _________ f

The Doppler Effect – a shift in the ____________________of a wave caused by _________________________between a ____________ and __________________.

4. The speed of the wave itself is _____________________________________________ .

3. The f is ____________ and the is ___________ if the

distance between observer and source is ____________

and ______________________ .

1. It is true for ______________________________ waves.

2. The __________ f of the source ______________________ .

6. __________ light has a shorter than ________ light.Light sources that are approaching an observer will

have ____________ and _____________ f . This is calleda __________ shift.

Light sources that are receding from an observer will have ____________ and _____________ f. This is called a __________ shift.

7. The faster the speed of the source or the observer, the _______the shift in and f.

5. If a sound source is approaching you, you will hear a sound with a __________________________ .If it is receding from you, you will hear a sound thatis _________________ .

Applications of the Doppler Effect:

1. radar: return time ______________________

Doppler radar ______________________

______________________

2. measure ____________________________ speeds

3. monitor _________________________

4. aid in diagnosis of ____________________________

5. red shift/blue shift of _____________________

6. measuring rotation of _______________________

7. ______________________________________________

Sonic booms – occur when _____________________exceeds the ________________________ in the medium.The wavefronts _______________ in a _________________that is dragged behind the ________________________ .The wavefronts _____________________ to produce a large ________________________________________.The same thing happens when a ____________ travelsfaster than the speed of _____________________ and leaves behind a _______________________ .

F. Diffraction – the _____________________into the regionbehind a___________________________________________ .

Diffraction is a property of ____________The waves can be: 1. _________________

2. _________________3. _________________4. _______________________________________

Diffraction is only significant when ______________________________________________________________________________________________

Ex. Plane waves incident on an opening:

plane waves

___ d, so the wave ________________.

w is different behind the opening?

Ex. Waves incident on an opening:

plane waves

_____ d, so _____________diffraction occurs.

w is different behind the opening?

ob

stacl

e

Ex. Plane waves diffracting ________________________

ob

stacl

e

Which example shows diffraction?

A

B

____ d

__ d ______________

Diffraction is explained by thinking of _______________within the opening as a ____________________ that createsnew ___________________ . The diffracted wavefront is the ____________________ of all of these wavelets from all the ______________________ within the opening. This idea was first explained by _________________________

Huygensplane waves

diffracted waves

AM vs FM: which diffracts more?Is that good or bad for reception?

typical AM frequency: _____________________

typical FM frequency: _____________________

Because ________ diffracts more, it can _________________

obstacles, so there are less ___________________________ .

AM ________ f ___________ _________ diffraction

So why does sound diffract ____________ than light?

And why do bass sounds diffract _________ than treble?

typical sound :____________________

typical visible light : __________________

Longer ’s diffract______________.

typical bass : ____________

typical treble : __________

Longer ’s diffract ___________.

Light can be made to diffract by making

________________________________________.

G. ____________________occurs when ____________ waves

(or pulses) are in the same ____________ at the same

______________.

Interference is a property of______________.

The waves can be:

1. _________________

2. ________________

3. ________________

4. ________________________________________

Principle of ______________________:

The results of interference are found by

adding the ________________________ of all the

waves at ____________________ in the medium.

Ex 1: The results of superposition can be found byadding the _________________ of each part of the pulse

+1

-2

+1

-2

-1

0

The ____________________ of these two pulses can be found be ________________ their two _______________ :

Shown here at themoment that they______________ .

resultantsuperposition

0

0

Ex 3:

Ex 4:

Ex 2:

The resultantsuperpositionwill look like:

Shown hereseparately asthey overlap:

Show below asseparate pulses:

Ex. 1: 2 sine waves, same f, _______________, unequal A’s

The superposition:

______________ interference – the resultant _______________have a ____________ magnitude because both waves move the medium in the __________ direction everywhere.

wave 1:

wave 2:

Ex. 2: Same f, 1800 ______________________, unequal A’s

The superposition:

wave 1:

wave 2: shifted ___or _______

______________ interference – the resultant _______________have a ____________ magnitude because both waves move the medium in the __________ direction everywhere.

Ex. 3: 2 waves, same f, 1800 out of phase, ___________A’s

The superposition:

_________________interference is _______________________ the resultant A ________________ everywhere

wave 1:

wave 2:

Ex 4: Same A, but at __________________________ f’s

_____________are a variation in _______________ caused bythe _____________________ of 2 waves whose frequencies____ and _____ are ________, but ________________ :

The amplitude of the envelope varies at the beat frequency:

beat frequency =

Ex. A 440-Hz tuning fork is struck while a stringvibrates at 443 Hz. What will be the beat f?

beat frequency =

Ex. A 256-Hz tuning fork is struck while a string vibrates. If beats occur at 2 Hz, what is the frequency of the string?

Ex 5: Waves X and Y exist in the same medium at the same time.

wave X

wave Y

+4

0

-4

+4

0

-4

+4

0

-4

+8

-8

Draw the interference of X and Y at points A-H:

A B C D E F G H I J K

Label each of the above points as constructive (C) or destructive (D)

Ex. 6: _____________________ occur as a result of the

___________________________ of ___________ waves that

have ___________________ frequency and _________________

amplitude are traveling in ____________________ directions

in ___________________ medium.

Ex: Typical patterns:

Although it appears to be _______________that

is _____________________ , it is actually made up of

_____________ that are interfering _____________________

and _____________________ at different points.

________________ - no displacement of medium;caused by ______________________ interference__________________ - maximum displacement of medium;caused by ______________________ interference

Each of these different patterns of possible standing

waves is called a ___________ :in

creasin

g__________in

creasi

ng

____

____

_____ nodes___ antinodes

___ nodes___ antinodes

___ nodes___ antinodes

mode 1:

mode 2:

mode 3:

Ex: If L = 4.0 m, how long is the wavelength?

Ex: If L = 5.0 m, how long is the wavelength?

Solve the 2 examples below for standing waves.

L

L

L =

Standing waves only occur at certain ___________

(special) ___________________ . These are determined by

the ______________________ properties of the system,

such as _______________, __________ , __________,

and the conditions at the ____________________ , also

known as the _________________ conditions.

During ___________________, an object is undergoing

standing waves that have a large ___________________

The special frequency at which this occurs is called

the _________________frequency of the object.

Ex: On air tube open_____________________, or a string tied down ________________:

Ex: An air tube closed __________________or a string tied___________________ :

In both examples above, the frequencies of all modes are_________________________ of the ________________ mode.

mode 1: ________________ mode 2: mode 3:

mode 2: mode 3:mode 1: ________________

In this case, the frequencies of all modes are NOT_________________________ of the ________________ mode.

Ex. Drum vibrations: