i. vibrations occur in: 1.______________________________________ 2....
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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:
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