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Physics 20 – Unit 4 – Oscillatory Motion and Mechanical Waves – FITB Notes General Outcomes:

I. I can _________________________________________________________________________ II. I can _________________________________________________________________________

_____________________________________________________________________________

Topic A – Period and Frequency Specific Outcomes:

I. I can _________________________________________________________________________ Oscillatory Motion

� Oscillatory motion is the ___________ back-and forth motion of an object (a cycle)

� One ___________ is one complete cycle of repetitive back-and-forth motion

� The object must return to the same ________ and _________ that it started with

� Nature has lots of oscillatory motion � Examples: pendulum of a clock, a dog wags its tail, a hummingbird flaps its

wings Frequency

� Frequency (Hz) is the number of _____________ that occur for an object per second:

ex. A source emits 20 cycles in 10 s. Find its frequency. ex. A pendulum swings from one end to the other in 0.75 s. Find its frequency. ex. A pendulum swings from one end to the equilibrium position (middle) in 0.0450 s.

Find its frequency. Period

� Period (s) is the time for one ____________ (cycle) to occur for an object:

ex. A source emits 20 cycles in 10 s. Find its period. ex. A pendulum swings from one end to the other in 0.75 s. Find its period. ex. A pendulum swings from one end to the equilibrium position (middle) in 0.0450 s.

Find its period.

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Period and Frequency

� Period and frequency have an _________ relationship:

� This gives us:

� A graph shows the inverse relationship:

ex. The frequency of a dog’s tail wag is 4.5 Hz. Find the time for one complete wag. ex. A clock pendulum makes one complete cycle in 1.0000 s. Find its frequency.

Topic B – Simple Harmonic Motion Specific Outcomes:

I. I can _________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________

II. I can _________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________

� Simple Harmonic Motion (SHM) is motion of an object, due to a _________ force that

is: � _________ proportional to the displacement from an equilibrium position � opposite in ____ to the displacement

� Restoring force is exerted by the ______! � Mechanical waves, simple pendulums and ____________ systems are examples of SHM � At each end:

� ___________ displacement from equilibrium � ________ potential energy (Ep) � ________ restoring force and _______ acceleration (Newton’s 2nd law: F = ma) � ______ kinetic energy (Ek), and ______ speed or velocity

� At equilibrium (middle) position: � ______ displacement � _______ potential energy (Ep) � ______ restoring force and ______ acceleration � ________ kinetic energy (Ek) and ________ speed or velocity

Topic C – The Simple Pendulum

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Specific Outcomes: I. I can _________________________________________________________________________

_____________________________________________________________________________ _____________________________________________________________________________

II. I can _________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________

� A ________ pendulum exhibits simple

harmonic motion � A simple pendulum has a mass, or

“_____” on it � Restoring force is the force exerted by

the pendulum to return the pendulum mass to its _____________ position

� Restoring force for a simple pendulum may be determined using _______ and SOHCAHTOA

� At one of the ends, the restoring force (FR) acts towards ____________

� _____________ or _____________ ex. Find the restoring force and acceleration for a 100 g pendulum that is pulled

sideways to an angle of 30º with the vertical.

� The period of a simple pendulum depends only on _______ of string and gravity:

ex. Calculate the period of a 4.0 m long pendulum. ex. Determine the acceleration due to gravity on an unknown planet if the period is

2.00 s for a string that is 1.5 m long. ex. What is the length of string used if the period is 4.78 s for a pendulum on Earth?

Topic D – Mass-Spring Systems

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Specific Outcomes: same as for topic C

� A mass-spring system exhibits simple _________ motion � It consists of a spring with one end connected to a wall and a _____ on the other end � Restoring force is the force exerted by the spring to return the mass to its

___________ position � _______ law is used with restoring force � Remember that restoring force is given by:

� Restoring force may be related to acceleration by ________ (Newton’s 2nd law) � A graph of force (F) vs. position (x) may be given, as follows:

� The average spring constant, k, is given by the _______ (k = BF/Bx) � The maximum speed for a mass-spring system occurs at the equilibrium position

(middle):

ex. A spring with a constant of 55.0 N/m is stretched +2.0 m. Determine the restoring

force.

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ex. A force of +1.0 N is exerted by a spring to restore it to equilibrium from a position

of -3.0 cm. Determine the spring constant. ex. A heavy spring (spring constant = 50 N/m) is attached to a mass of 0.250 kg.

a) Determine the acceleration of the mass-spring system when the displacement is 0.10 m [right].

b) Calculate the maximum speed of the mass if the spring can stretch to a

maximum distance of 0.500 m.

� The period of a mass-spring system depends only on the spring constant and mass:

ex. A heavy spring (spring constant = 50 N/m) is attached to a hanging mass of 0.250 kg. Determine the period of the mass-spring system.

ex. Find the spring constant if a 17 g mass takes 12 seconds to make 100 oscillations.

Topic E – Mechanical Waves Specific Outcomes:

I. I can _________________________________________________________________________ _____________________________________________________________________________

II. I can _________________________________________________________________________ III. I can _________________________________________________________________________

_____________________________________________________________________________ IV. I can _________________________________________________________________________

_____________________________________________________________________________ Simple Harmonic Motion

� A mechanical wave is the simple harmonic motion of _______ particles in a medium ex. water, sound

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� There are two main types: � ___________ � ___________

� We will look at these in more detail later � A wave ____ is a section of a mechanical wave:

� It has __________ (A), which is the maximum displacement of the wave � A ____________ (λ) is the shortest distance a wave pattern repeats itself

� ______ are in the middle, and __________ are at the ends � There are three possible ways to measure wavelength for a wave:

1. from trough to adjacent trough (antinodes) 2. between three consecutive nodes 3. from crest to adjacent crest (antinodes)

� Two points on a wave are said to be “_________” if they are traveling in the same direction and are the same distance from the “rest position” (flat line):

Wave-Front vs. Ray

� Huygens envisioned EMR as waves through his model called Huygens Principle: a) a wave front (line-shape) is made of many small point sources of tiny secondary

waves called ________ (round circles)

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b) wavelets _________ outward in a concentric circle at the same speed as the wave itself

c) a line _________ to all the wavelets constitutes a wave front

� Moving waves may be viewed as a wavefront: � Moving waves may also be viewed as a ray, in the same direction:

� Rays are __________ lines indicating the direction of a wave front (perpendicular)

� Rays that spread out are ___________ rays � Rays that intersect are ___________ rays � A _____ _______ is a location where circular waves may

originate � Rays ________ out from a point source

Reflection � There are four main properties of mechanical waves: reflection, refraction,

diffraction and interference � We will start looking at these in Physics 20; they will be fully developed in Physics 30 � We will use ___ _______ to show how mechanical waves interact with barriers and

different media � We will study how mechanical waves ________ with surfaces or barriers � ________ waves or rays approach a surface; _________ waves or rays leave a surface � Angle of __________ - angle between the incident ray and the normal � Angle of __________ - angle between the reflected ray and the normal � The _______ is an imaginary line that is perpendicular to a surface (90º) � Laws of Reflection:

� Angle of incidence is always _____ to the angle of reflection � Incident ray and reflected ray are always in the same _____ (2D)

� Geometry angles apply here (triangles, etc.) � Mechanical waves are __________ when they hit a barrier � If waves hit a barrier at an angle of zero, they are reflected back in the opposite

direction:

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� If mechanical waves strike a barrier at an angle, they will reflect at the same angle

(Laws of Reflection):

Topic F – Universal Wave Equation Specific Outcomes:

I. I can _________________________________________________________________________ II. I can _________________________________________________________________________

_____________________________________________________________________________ III. I can _________________________________________________________________________

_____________________________________________________________________________ _____________________________________________________________________________

Speed of a Mechanical Wave

� Taking the average speed equation v=Bd/Bt, we can substitute in the length of a wave train, l, for Bd to get:

ex. A wave travels at 10 m/s. It takes 3.4 seconds for the entire wave to pass a motion sensor. Determine the length of the wave.

ex. A 75.0 cm long wave pulse takes 4.8 seconds to pass any point in a spring. How

quickly is the pulse traveling through the spring? ex. A student on the ground yells at his friends who are standing at the base of a tall cliff.

The speed of sound is 340 m/s, and it takes 4.2 seconds for the student to hear his own echo. Determine how far the student is from his friends.

Universal Wave Equation � The universal wave equation relates speed of a mechanical wave to frequency and

wavelength:

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ex. A wave train has a wavelength of 1.2 m and a frequency of 60 Hz. Determine its

speed. ex. Find the wavelength if a wave with a frequency of 13.7 Hz travels at a speed of 20

m/s. ex. The distance between successive crests in a series of water waves is 1.5 m and the

wave travels 6.5 m in 2.8 s. Calculate the frequency of a surfer bobbing up and down in the water.

Topic G – Transverse and Longitudinal Waves

Specific Outcomes:

I. I can _________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________

II. I can _________________________________________________________________________ _____________________________________________________________________________ _____________________________________________________________________________

Wave Medium

� A wave medium is composed of the particles that are __________ in a wave � The overall motion of the wave medium is ________ for any type of wave � ____________ is the vibration motion of the wave, unique for the type of wave � A ______ will propagate differently, depending on if it is transverse or longitudinal � If transverse, it will propagate ___________ to the motion of the wave medium � If longitudinal, it will propagate ___________ to the motion of the wave medium

Transverse vs. Longitudinal � A transverse wave is described by the following properties:

� particles of the wave medium vibrate ____________, perpendicular to the direction of wave motion

� wave is made of ______ and ______ � occurs in ______ or ______

� A longitudinal wave is described by the following properties:

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� particles of the wave medium vibrate ______________, parallel to the direction of wave motion

� made of ____________ and ____________ � occurs in solids, liquids or gases

� _______ of a transverse wave correspond to the ____________ of a longitudinal wave:

Transverse Pulse vs. Wave � A transverse pulse is a single _____________ in a medium, with no simple harmonic

motion:

� If the pulse repeats (__________), it has simple harmonic motion:

Inversion of a Wave � If a pulse travels in a medium, it will ________ upon hitting a barrier � The inverted pulse will travel in the ___________ direction

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� _________ also applies to transverse and longitudinal waves � Upon reflection with a barrier:

� for a transverse wave, ______ become ______ and vice versa � for a longitudinal wave, _____________ become _____________, and vice versa

Topic H – Wave Medium and Energy Specific Outcomes:

I. I can _________________________________________________________________________ _____________________________________________________________________________

II. I can _________________________________________________________________________ Wave Medium

� The medium is made of the particles that ___________ (vibrate) � The medium can be:

� ________ or deep (ex. water) � ______ (____ density) or dense (____ density)

� A wave can move from one ________ to another, through a change in density � If a wave moves from one density to another, the following will happen:

� _________ stays the same (constant) � ______ and ___________ either increase together or decrease together

� This is consistent with the universal wave equation (_____) if frequency, f, is constant � If a wave moves from shallow to deep water, or from high density to low density:

� wavelength __________ � speed __________

� If a wave moves from deep to shallow water, or from low density to high density: � wavelength __________ � speed __________

� In moving from a less dense medium to a more dense medium, a portion of the incident wave is _________ and _________:

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Wave Energy � A matter wave may transfer a large amount of energy through:

� high ______ (kinetic energy), or � high __________ (potential energy)

� An electromagnetic wave (at the speed of light) may transfer a large amount of energy through:

� ____ wavelength (____ frequency)

Tsunami Waves � Tsunami waves are large _____________ of water, deep in the ocean (often caused by

an earthquake or fault line) � In the deep ocean, tsunamis have:

� ____ speed, so they have high kinetic energy � ____ amplitude, so they are not usually visible on the surface

� When approaching shallow water, tsunami waves _____ _____ and wavelength ___________

� In shallow water, a tsunami’s kinetic energy changes into _____________ potential energy

� This is seen as a very high ___________ wave, which explains why a tsunami is tall only when near a beach!

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Topic I – Constructive and Destructive Interference Specific Outcomes:

I. I can _________________________________________________________________________ _____________________________________________________________________________

II. I can _________________________________________________________________________ Superposition

� Two or more _________ waves may overlap (combine) temporarily to form either: � a wave that has a ______ amplitude than the original waves, or � a wave that has ______ amplitude than the original waves

� Once the waves ____ each other, they return back to their original amplitudes � Principle of Superposition = when two or more waves combine, the amplitude of the

resultant (vector addition) wave is the ____ of the amplitudes of the individual waves � The amplitude of a transverse wave is treated as a vector:

� from equilibrium to a crest it is ___ � from equilibrium to a trough it is ___

Interference � Remember that waves that are “_________” are on the same side of the equilibrium

position, but travel in opposite directions � Constructive interference = when two or more in phase waves overlap to form a

temporary wave with a higher amplitude:

� After superposition, the two individual waves possess their original amplitudes:

� Two waves that are “____________” are on the different sides of the equilibrium position

� Destructive interference = when two or more out of phase waves overlap to form a temporary wave with a lower amplitude:

� After superposition, the two individual waves possess their original amplitudes:

ex. Two waves of amplitude 5.0 cm and 8.0 cm interfere. Calculate the magnitude of amplitude for superposition, if the original waves are:

a) in phase

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b) out of phase

� Remember that a point source may form a series of circular wave fronts:

� Two ______ sources, placed side by side, will produce a pattern of interference:

Topic J – Mechanical Resonance Specific Outcomes:

I. I can _________________________________________________________________________ Nodes and Antinodes

� Each transverse wave contains: � _________ = points of zero amplitude caused by destructive interference (at

the rest position) � _________ = points of maximum amplitude caused by constructive interference

(at the top and bottom) � Two transverse waves with antinodes that are out of phase:

� Destructive interference occurs:

� Here, the two waves are staggered by ____, so they seem to cancel out � Two transverse waves with antinodes that are in phase:

� Constructive interference occurs:

Standing Waves � A wave formed by ____________ interference is called a standing wave � A standing wave pattern requires two overlapping transverse waves to be:

� approaching each other (i.e. _________ directions) � _________ (i.e. on the same side of the equilibrium position line)

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� Standing waves make it appear that a wave is in the _____ location � In reality, two waves move ________ one another � The antinodes of the two waves simply ____ together while they are overlapping

ex. The distance between adjacent nodes on a standing wave is 1.50 m. The frequency

is 50.0 Hz. a) Calculate the wavelength. b) Calculate the speed of the wave.

ex. The distance between the second node and the sixth node is 50 cm. Find the wavelength of the wave.

Forced Frequency � A pendulum’s amplitude may be altered by two different means:

� _______ frequency � __________

� Over time, a pendulum’s amplitude becomes reduced because ______ is lost � Frequency and _______ remain the same, since they do not depend on energy � The frequency of a pendulum is based on ______ and gravity � The amplitude may be corrected by having another object apply an ______ non-zero

net force to the pendulum (physical contact) � The term for this is “______ frequency” because the external force is applied at the

same frequency as the pendulum itself � The external object must physically be ____________ to the pendulum � The higher the external force, the _______ the amplitude of the pendulum

Dampening � The pendulum may also reduce its amplitude, by doing _____ on its surroundings � This means a _____ of energy by the system � Since amplitude is being reduced, the pendulum is being __________

Resonant Frequency � All matter ________ (oscillates) � Each object has a natural frequency at which it vibrates, called the _________

frequency � The physical __________ of each object determine this resonant frequency � The amplitude is quite ____, so we don’t usually notice the oscillation

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� If a forced frequency matches the natural resonant frequency object well, it may create a very _____ amplitudes

� If this happens, we have reached ___________ resonance � The effect may tear the object apart

Pendulums � All pendulums of the same _______ vibrate at the same frequency, regardless of mass � Two pendulums with different lengths vibrate at different __________ frequencies � _______ and temperature changes can affect the amplitude of a pendulum � The resonant frequency of a ________ depends only on its length � If two pendulums are connected to the same surface, one pendulum may _________

the amplitude of the other pendulum through mechanical resonance:

Quartz Crystals � Quartz crystal is a _______ naturally found in the Earth’s crust � Quartz crystals are _____________; they oscillate when a voltage is applied to them � A quartz crystal only needs a _______ to keep the oscillation constant � At the correct voltage, the oscillation may have a period of exactly __ second � Quartz crystals are used in clocks, because they:

� can be cut very ______ � have a very _________ oscillation

� Artificial ________ crystals may also exhibit a piezoelectric effect � __________ science studies this property

Bridges and Towers � An office tower needs to be designed so that the wind’s ___________ does not match

the natural resonant frequency of the building � Bridges are designed to allow wind to ____ _________ as much as possible � Newer buildings incorporate _______ (ex. pools of water, giant swaying masses) � A bridge may _______ if the wind’s oscillation matches

ex. Tacoma Narrows bridge � ___________ may also affect towers and bridges

ex. Taipei 101 tower in 2008

Topic K – Acoustic Resonance Specific Outcomes:

I. I can _________________________________________________________________________ _____________________________________________________________________________

Musical Resonance

� Acoustic resonance makes the different _____________ possible for a musical instrument

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� At its resonant frequency, a musical instrument vibrates with _____ amplitude! � A musical instrument usually has _________ resonant frequencies, organized into a

fundamental frequency and its overtones � For musical objects, a wave is __________ because it is symmetrical

ex. the following waveform corresponds to 1.5 wavelengths, not 3 wavelengths!

Vibrating Strings � The lowest resonant frequency of a string is called the _____________ frequency

� This resonant frequency (f) is for ____ � This string vibrates as ____ whole segment � The second resonant frequency is also called the first overtone:

� This resonant frequency (f) is for λ � The third resonant frequency is also called the second overtone:

� This resonant frequency (f) is for ______

Air Column Resonators � If a ______ source is held near a column of air, it can make the air column resonate � The air column may resonate in more than one place � There are two types of column resonance:

1. ______ tube (or open pipe) 2. ______ tube (or closed pipe)

� Lengths of an air column at which this occurs are called resonant _______ � The __________ heard or measured depends on the length of column used � Resonance will occur only if there is _____________ interference between the sound

source and the column � The column of air:

1. always has a ______ source (ex. speaker, tuning fork) at one end 2. either be left open (exposed) or closed (________) at the other end

� A closed-pipe (closed-_____) resonator is a cylindrical tube of air with one end closed � Constructive interference (resonance) occurs if there is an _________ at the sound

source � At resonant lengths of the column, constructive interference (_________) occurs � The shortest (fundamental) resonant length of a closed-tube column is ¼λ (or λ/4):

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� For each additional half ____________ (λ/2 or 2λ/4), there is another resonant length � The resonant lengths of a ______-tube resonator are λ/4, 3λ/4, 5λ/4, etc.

ex. If the shortest (first) resonant length for a closed pipe resonator is 16.5 cm when a

500 Hz tuning fork is used, what is the speed of sound? ex. If the first resonant length in a closed air column is 18.5 cm when sounded with a

480 Hz tuning fork, what is the speed of sound?

� An open-pipe (open-tube) resonator is a cylindrical tube of air with _____ ends open � Same as before: constructive interference (resonance) occurs if there is an ________

at the sound source (at resonant lengths) � The _________ resonant length for an open-tube resonator is ½λ or λ/2 � Each additional ____ wavelength (λ/2) yields other resonant lengths � The resonant lengths of an open-tube column are λ/2, 2λ/2, 3λ/2, 4λ/2, 5λ/2, etc. � Simplified, this gives us resonant lengths of λ/2, λ, 3λ/2, 2λ, 5λ/2, etc. � The first three resonant lengths

� Let’s do a side-by-side comparison of the resonant lengths in closed-tube and open-tube resonance columns:

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ex. Find the shortest length of an open tube air column that will resonate at 400 Hz

with a speed of sound of 341 m/s.

Vibrating Strings � A vibrating string will be governed by the first resonance equation for an open-pipe:

Topic L – The Doppler Effect Specific Outcome:

I. I can _________________________________________________________________________ _____________________________________________________________________________

� If a stationary (not moving) _____ source emits sound waves, they appear as follows:

� If a sound source is not moving, the waves that are emitted follow equation _____ ex.If sound is emitted at 300 m/s with a frequency of 75 Hz, the wavelength would be

____ using v = fλ. � If the sound source were moving _____ from you or ________ you, what would be

different? � If a point source moves while it emits sound waves, they appear as follows:

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� If the object is moving towards you: � its waves are compressed (_______ λ) � its frequency is increased (_______ f)

� If the object is moving away from you: � its waves are stretched (_______ λ) � its frequency is decreased (_______ f)

� This is called the Doppler effect � It explains why an ambulance:

� has a ______ pitch as it approaches you � has a much ______ pitch once it passes

� If an object moves while it emits waves, its frequency is Doppler _______ by its _______

� The Doppler effect is described by:

� Shifts: towards = _______ f, away = _______ f � A source that moves towards you (higher frequency) will be solved with equation:

� A source that moves away from you (lower frequency) will be solved with equation:

ex. Calculate the change in pitch of an ambulance. The ambulance travels at 25.0 m/s with a siren that whistles at 300 Hz. Assume the speed of sound in the air is 330 m/s.

� The speed of sound is about ____ m/s (Mach 1) � If a source moves at Mach 1, it breaks the sound barrier and produces a “_____

_____” � This happens because of a _____ shockwave

� This also causes a cone of condensing ______ vapour, shaped like the shockwave � Once the sound barrier is __________, the condensation cone goes away � If a source moves _______ than the speed of sound, it produces an even more

dangerous shockwave, shaped like a ________ � This may travel along the ________, and damage buildings

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� The shockwave is formed by the addition of the individual ______ _______ into a triangular shape (ex. bullets, shells)

ex. shockwave formed by the Thrust SSC as it broke the land speed record (and the

sound barrier) � The Doppler effect also applies to how stars are ___________ with the __________ of

the universe