Unit 11
Vibrational Motion
 Wiggles, vibrations, and oscillations are an inseparable
part of nature.
 Much of what we see & hear is only possible because of
vibrations and waves.
 In this Unit we will explore vibrational motion and its
relationship to waves.
Periodic Motion
 A vibrating object is wiggling back
and forth about a fixed position.
 Like the mass on a spring, the mass
moves up & down in a regular and
repeated path.
 In Physics, a motion that is regular
and repeating is referred to as
periodic motion.
Periodic Motion
 Periodic motion – moving back &
forth, vibrating, oscillating at
repeated and regular intervals
 What are some other examples of
periodic motion?
Sinusoidal Nature of Vibration
 Suppose that a motion detector was placed
under the mass in order to detect the
changes in position over time.
 A position vs. time graph of the periodic
motion would look like this…
Sinusoidal Nature of Vibration
Resting
position
 Characteristics:
 Sine wave – vibrating back/forth about a fixed resting position
 Periodic – regular repetitive motion
 Dampening – energy is being dissipated; max & min decrease
over time (not slowing down!)
Period
 Period – time is takes to complete 1 full cycle
 Seconds / cycle
 A full cycle of vibration can be thought of as
movement from resting position (A) to its max height
(B) down to its min position (D), and back to resting
position (E).
Period
 Using this graph, it is possible to determine to time it
takes to complete a 1 full cycle or period.
 Standard unit – second (s)
 From position A to E it takes 2.3 seconds
 If the motion is periodic (regular & repetitive) then it
should take 2.3 s to complete any of the cycles!
1st
A to E
0.0 s to 2.3 s
Cycle
Time
(seconds)
2.3
2nd
E to I
2.3 s to 4.6 s
2.3
3rd
I to M
4.6 s to 6.9 s
2.3
4th M to Q
6.9 s to 9.2 s
2.3
5th Q to U
9.2 s to 11.5 s
2.3
6th U to Y
11.5 s to 13.8 s
2.3
Cycle Letters
Times at Beginning and
End of Cycle (seconds)
Amplitude
 Amplitude – the max displacement of the
mass from its resting position.
 Dampening – energy is being dissipated;
max & min decrease over time
 Therefore the mass does not slow down,
but it is the amplitude that decreases as
time passes.
 Amplitude is a reflection of the amount of
energy possessed by the vibrating object.
Larger the amplitude the more energy it
has!
Frequency
 Frequency– number of complete cycles per unit of
time.
 Frequency = # of cycles / second
 Standard units of frequency is Hertz (Hz)
Frequency
 The concept of frequency is best understood if you
associate it with its everyday meaning.
 Frequency is a word we often use to describe how often
something occurs.
 You might say that you frequently check your email or
frequently talk with a friend.
 Frequency refers to how often a repeated event occurs.
Frequency
 A 256 Hz tuning fork makes 256
back & forth vibrations each
second!
 A 512 Hz tuning fork has an
even higher frequency; you
could say it vibrates faster at 512
cycles/second!
 In comparing these 2 tuning
forks its obvious that the one
with the higher frequency has
the lowest period.
256 Hz
512 Hz
*Higher the frequency the lower the period
Period vs. Frequency
 Therefore we can say that period and frequency have
an inverse relationship…in fact they are reciprocals of
each other.
 Period = time is takes to complete 1 full cycle
(seconds / cycle)
 Frequency = # of cycles per unit of time
(cycles/sec.)
Period vs. Frequency
 To better understand the distinction consider the
following:
 Tim Ahlstrom holds the record for hand clapping…
 793 times in 60 seconds.
 What is the frequency and what is the period of Tim’s
hand clapping? 1 clap = 1 cycle
Frequency = 793 cycles / 60 sec. = 13.2 Hz
Period = 60 sec / 793 cycles = 0.0757 seconds
Pendulum Motion
Pendulum Motion
Check for Understanding
 Determine what point has the greatest…
 Force of gravity? Everywhere the same!
 Speed? C
 Potential energy A
 Kinetic energy C
 Total mechanical energy Everywhere the same!
Check for Understanding
 Us conservation of energy to fill in the blank
0.4
2.4
0
2.4
Waves
 Waves are everywhere! We encounter them on a daily
basis…
 Sound waves
 Light waves
 Radio waves
 Microwaves
 Water waves
 We study waves because it gives us a glimpse into the
nature of reality and helps us to understand how the
physical world works.
Nature of Waves
 So waves are everywhere, but what makes a wave a
wave?
 What characteristics, properties, or behaviors are
shared by waves?
 Waves can be described as a disturbance that travels
through a medium from one location to another.
Nature of Waves
 Lets consider a stretched slinky…
 To introduce a wave to the slinky, the first particle is
moved from is rest position creating a disturbance.
 The particle might be moved up & down or forward &
backward, but once moved, it returns to its rest position.
 A single disturbance moving through a medium from one
location to another is referred to as a pulse.
 A repeating & periodic disturbance is called a wave.
Medium
 What is a medium?
 Medium is a substance or material that carries the
wave (or disturbance) from one location to another.
 The wave medium is not the wave nor does it make the
wave; it merely transports the disturbance from here to
there…
 What is the medium in a slinky wave? The slinky coils
 In an ocean wave? The ocean water
 In a sound wave? The air
 In a stadium wave? The fans
Particle to Particle Interaction
Energy Transport
 When a waves moves through a medium, the individual
particles of the medium are displaced from their rest
position, but eventually returns to the original
equilibrium position.
 Therefore, a wave is said to transport energy and not
matter!
Categories of Waves
 One way to categorize waves is on the basis of the
direction of the particles of the medium relative to the
direction of the disturbance or wave.
 Wave types:
 Longitudinal waves
 Transverse waves
 Surface waves
Longitudinal Waves
 A longitudinal wave is a wave in which particles of
the medium move parallel to the direction of the
wave.
Longitudinal Waves
 A sound wave traveling through the air is a classic
example of a longitudinal wave.
 Sound is a pressure wave in the air particles causing
them to vibrate back and forth starting a chain
reaction in the air.
Longitudinal Waves
 The direction of the vibrating air particles are parallel
to the direction of the wave.
 The wave is propagated through the air until the sound
wave reaches the ear of the listener.
Transverse Waves
 A transverse wave is a wave in which particles of the
medium move perpendicular to the direction of the
wave.
Surface Waves
 A surface wave is a wave in which particles of the
medium move in a circular motion.
 Only the particles of the at the surface of the medium
move.
Electromagnetic vs. Mechanical
 Another way to categorize waves is by their ability or
inability to transmit energy through a vacuum.
 Electromagnetic waves (aka light) is a wave capable
of transmitting energy through a vacuum (empty
space) and do not need a medium to travel.
Long wavelength
Low frequency
Short wavelength
High frequency
Electromagnetic vs. Mechanical
 Mechanical waves are not
capable of transmitting
energy through a vacuum.
 They require a medium in
order to transport their
energy from one location to
another.
 A sound wave is an example
of a mechanical wave and
therefore incapable of
traveling through a vacuum!
IN SPACE
Anatomy of a Transverse Wave
 Crest – highest point of the wave
 Trough – lowest point of the wave
 Amplitude – max amount of displacement from rest (rest to crest)
 Wavelength (λ) – length of one complete wave cycle (crest to crest)
 A to E
 D to G
 B to F
Anatomy of a Longitudinal Wave
 Compression – point on a longitudinal wave where the particles of the
medium are most dense (compact).
 Rarefaction – point on a longitudinal wave where the particles of the
medium are least dense.
 Wavelength (λ) – length of one complete wave cycle
 A to C (compression to compression)
 B to D (rarefaction to rarefaction)
The Wave Equation
V=
λf
Speed = Wavelength • Frequency
v – velocity or speed of a traveling wave
λ - wavelength in meters (m)
f – frequency in Hertz (Hz)
Law of Reflection
 Reflection occurs when a wave bounces off an object,
barrier, or surface.
 Waves will always reflect in such a way that the angle
at which they approach the barrier equals the angle at
which they reflect off the barrier.
The angle of
incidence is equal
to the angle of
reflection.
Refraction
 Refraction is the bending of a wave caused by the
change in speed of a wave as it passes from one
medium to another.
Water waves travel fastest when the
medium is deepest. Thus, if water waves
are passing from deep into shallow water,
they will slow down. The decrease in
speed will be accompanied by a decrease
in wavelength and direction change or
bending of the waves.
Diffraction
 Diffraction is the change in direction of waves as they
pass through an opening or around a barrier in their
path.
Interference
 What happens when two waves meet?
 What effect will the meeting of the waves have upon
the medium?
 Will the two waves bounce off each other or will they
pass through each other?
 These questions involving the meeting of two or more
waves pertain to the topic of wave interference.
Interference
 Wave interference occurs when two or more waves
meet or combine while traveling through the same
medium.
Constructive Interference
 Constructive interference is a type of interference
where the waves combine so that the resulting wave is
bigger than the original waves.
In phase
Destructive Interference
 Destructive Interference is a type of interference where
the waves combine so that the resulting wave is smaller
than the largest of the original waves.
Out of phase
Check for Understanding
 Categorize each labeled position along the medium as
being a position where either constructive or
destructive interference occurs.
G, J, M, & N – Constructive
H, I, K, L & O - Destructive
Check for Understanding
 Twin water bugs Jimminy and Johnny are both creating a series of circular
waves by jiggling their legs in the water. The waves undergo interference and
create the pattern represented in the diagram. The thick lines in the diagram
represent wave crests and the thin lines represent wave troughs. Several of
positions in the water are labeled with a letter. Categorize each labeled position
as being a position where either constructive or destructive interference occurs.
A & B – Constructive
C, D, E, & F - Destructive
Doppler Effect
 The Doppler effect can be described as the effect
produced by a moving source of waves in which
frequency appears to increase or decrease relative to an
observer.
 If the source is moving towards an observer, frequency
appears to increase.
 If the source is moving away from an observer, the
frequency appears to decrease.
 It is important to note that the effect does not result
from an actual change is frequency of the source.
Doppler Effect
 The Doppler effect can be observed for any type of
wave – water, sound, light, etc.
Low pitch
High pitch
http://www.youtube.com/watch?v=Kg9F5pN5tlI
http://www.youtube.com/watch?v=Y5KaeCZ_AaY
Red Shift
 The Doppler effect is of intense interest to astronomers who use
the information about the shift in frequency of electromagnetic
waves produced by moving stars in our galaxy and beyond in
order to derive information about those stars and galaxies. The
belief that the universe is expanding is based in part upon
observations of electromagnetic waves emitted by stars in distant
galaxies. Furthermore, specific information about stars within
galaxies can be determined by application of the Doppler effect.
Galaxies are clusters of stars that typically rotate about some
center of mass point. Electromagnetic radiation emitted by such
stars in a distant galaxy would appear to be shifted downward in
frequency (a red shift) if the star is rotating in its cluster in a
direction that is away from the Earth. On the other hand, there is
an upward shift in frequency (a blue shift) of such observed
radiation if the star is rotating in a direction that is towards the
Earth.
Standing Waves
http://www.youtube.com/watch?v=-gr7KmTOrx0
http://www.youtube.com/watch?v=VXp1IvdSKkw
Standing Waves
 A standing wave is a stationary wave confined to a
given space.
 The medium vibrates back & forth from positive
displacement to negative displacement.
 Points of the medium that never move (no
displacement) are known as nodes.
Harmonics
 Standing waves are created
when the source wave
interferes with the returning
reflected wave.
 Standing waves occur only at
specific frequencies of
vibration called harmonics.
Harmonics
2nd Harmonic
1st Harmonic
5th Harmonic
3rd Harmonic
4th Harmonic
Cymatics
 Cymatics is the study of visible sound and vibration.
http://www.youtube.com/watch?v=GtiSCBXbHAg
Applications of Waves
http://physics-animations.com/Physics/English/wav_txt.htm