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 pendulum bob at points A, B and C. B A C At A: At B: In all 3 cases, F net ___________________. 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 w equilibrium   This component is ______________ to the motion and is ____________ in direction to the ____________

Ex 2: Vibrating mass m on a spring with constant k : m m equilibrium spring Draw the forces that act on the mass at the points shown: Except at x = 0, F net ____________________________ F S _________________ as x increases F S pulls the mass back towards __________________ F S is also a ______________________ force. x x compression 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 2 nd 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 10 complete 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 = =  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 = 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 of a simple pendulum? Ex: What determines the natural frequency of a 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 __________________. _____________ source disturbs the medium 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's amplitude 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 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… 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… 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 (360 0 ) apart or a multiple of 1 are said to be ____________________ Two points on a wave that are (½) (180 0 ) 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 completely out 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 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 temps because ______________________________________. 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 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 a wavelength 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:

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 called the ____________ 3. This is the ___________ The ____________ wave's frequency has been ______________ by wave 1.

Do not confuse radio waves sent as ___________________ waves with sound waves, which are ___________________ waves. antenna or satellite transmits ________ 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 on a radio ________ energy  ___________energy  ________ energy

Ex. String (or wind) instruments are played by making the string (or tube) _____________________________. v = f v is _________________ for a fixed tension. Shorter string   _____________  f ___________ 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. bug side view of 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 = surfaces with ____________________ Far away, the wave velocity vectors become ____________

old wavefront is __________________ Now bug moves left while jumping at a constant frequency 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 called a __________ 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 that is _________________.

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 ____________ travels faster than the speed of _____________________ and leaves behind a _______________________.

F. Diffraction – the _____________________into the region behind 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?

obstacle Ex. Plane waves diffracting ________________________ obstacle

Which example shows diffraction? A B ____ d __ d  ______________

Diffraction is explained by thinking of _______________ within the opening as a ____________________ that creates new ___________________. The diffracted wavefront is the ____________________ of all of these wavelets from all the ______________________ within the opening. This idea was first explained by _________________________ Huygens plane 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 by adding the _________________ of each part of the pulse The ____________________ of these two pulses can be found be ________________ their two _______________ : Shown here at the moment that they ______________. resultant superposition 0 0

Ex 3: Ex 4: Ex 2: The resultant superposition will look like: Shown here separately as they overlap: Show below as separate 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, ______________________, 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, 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 by the _____________________ 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 string vibrates 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 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 ___________ : increasing__________ ___ 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: