Vibrations and Waves
A ____________ is a wiggle in ____________. While this
definition is ________, it doesn’t really say much. A better
definition is when an object moves ________ and __________
over the same ________________ over and over.
Vibrations are different from __________, which occur when
energy produced by a vibration can ________ ________ from its
vibrating source.
All waves are caused by ____________________.
Vibrations and Pendulums
_____________ was very interested in pendulums. Using his
_________ as a timer, he discovered that the ____________ (time
for one complete swing; symbol = ____) depends only on the
____________ of the pendulum and gravity. Importantly,
________ is not involved. That means that these two pendulums:
will have the same ____________, a fact that will blow the mind
of a ______-______________ _______.
Elegantly, this statement can be T =
When the above equation is graphed, it will generate a
__________. To get a straight line, you should graph period vs.
_________ ____________ of length. This is because all straight
lines have an equation of the form: __________ = _________ x
_________ + __________. (I’m not looking for y = mx+b; be
more generic.)
The distance from equilibrium for a pendulum is called its
__________________.
Wave Description and Anatomy
If you attached a pendulum with a marker, and allowed the marker
to contact a paper moving at constant speed, the shape drawn will
be a ________ __________. This shows a
__________________ ____________ can create a ________ if
given an outlet for its ___________.
A single disturbance flowing through a medium is called a
__________. A picture might look like this:
A wave is different. A wave is made up of many
_______________________ equally ____________ and
__________. A picture might look like this.
Most waves have a ____________, or substance through which
they travel. This medium does not __________ the wave, nor is it
the wave. The wave itself is the ____________. For waves to be
able to travel through a medium, the medium’s
__________________ must be able to ________________.
Before a wave passes through, a medium is in an undisturbed state
of _____________________. Movement from this state represents
____________ passing through the medium.
Areas of maximum positive displacement are called
____________. Similarly, areas of ______________
________________ displacement are called ______________.
__________________ of a wave refers to the distance from
______________________. It is really incorrect to ask “What is
______ amplitude of a wave. Amplitude at a certain position
______________ all the time. One can only ask what is the
amplitude of the wave at a ______________ position at a certain
________.
____________________ is the distance taken up by one
________ __________________. The symbol for wavelength is
____. It consists of the distance covered by one full upper part and
one full lower part of a wave.
The __________________ of a wave is the ____________ of
__________ that pass in a given ________ _____________
(usually 1 second). Then the time interval is 1 second, the unit on
frequency is ___________.
For example, if an observer calculates 2 waves going by a certain
point each second, the frequency can be calculated using the
formula
Frequency = ___________________
like this:
The period is related to the frequency. Actually they are
______________________ of each other. So, in the above
example the period would be:
Wave Motion and Energy Transport
There are two ways to transport energy from point A to point B.
1. _______________ method of energy transport: This
method uses an object (______________) to make the
entire journey with the energy. Some examples might
be:
2. _______________ method of energy transport: This
method uses a substance (______________) that spans
the distance from point A to point B to pass energy
along particle to particle until it is finally unloaded at
point B. Some examples might be:
In wave energy transport, individual particles only
______________; they do not travel. That is, at the end of the
disturbance, they will still be in the ________ __________ as they
______________.
The energy a wave is carrying is evident in the wave’s
__________________. This only makes sense, since to make a
large __________________ it would take a large _______.
However, the non-physics type would be baffled by the
relationship between energy and amplitude. If waves A and B are
both traveling through the same material, but wave B is 3 times as
tall as wave A, wave B is actually carrying _____ times the energy
as wave A, not ______ times like the non-physics type would
think. The relationship between energy and amplitude is a
d____________ s___________ relationship.
Wave Speed
The speed of a wave (symbol = ______) depends on ONE thing:
the ____________ through which it travels!
For example, waves travel faster in ______ water than they do
through _____________ water. Likewise, waves travel faster
through a spring under greater ______________ then they do
through a spring with little.
To calculate wave speed, we use an old equation
speed = _____________
but with new wave vocabulary:
wave speed = _______________ or _____________ x _________
For example: If a wave has a frequency of 5.0 Hz, and a
wavelength of 1.5 meters, what is the wave speed?
If nothing changes regarding the medium, the ________
__________ will not change. If in that case if the frequency is cut
in half, what will happen to the wavelength?
Transverse and Longitudinal Waves
Waves can be classified into three types.
1. __________________ waves have the medium moving at a
right angle to the wave speed (energy movement). A
transverse wave would look like this:
2. _________________ waves have the medium moving
parallel to the wave speed (energy movement). A transverse
wave would look like this:
3. _________________ waves are combinations of both
longitudinal and transverse waves. They form on the surface
of fluids like water. Particles in a surface wave move in
______________. The wave ___________ when there is no
longer enough room for the particle to complete its circle.
Transverse waves travel based on one particle’s ability to
________________ the next particle, or do ________ on the next
particle. These waves travel great through ______________ and
the edges of ______________ because the particles are somewhat
attached to each other. However, they do not travel well through
the middle of ____________, because particles are very ineffective
at passing energy on.
Longitudinal waves are made up of areas of higher than normal
pressure (______________) and areas of lower than normal
pressure (_______________). These waves use
______________________ to pass energy from particle to
particle. Because energy is passed easily from particle to particle,
these waves can travel through both ____________ and
______________.
Interference
When waves try to ___________________________ influence the
same _____________, interference results.
When two waves overlap so that they both try to move a medium
particle in the same direction, we get ______________________
interference. We say that two waves that line up crest on crest like
this are ____-___________, and would look like this:
When two waves overlap so that they both try to move a medium
particle in different directions, we get ______________________
interference. We say that two waves that line up crest on trough
like this are _____-____-___________, and would look like this:
Standing Waves
Any time a wave hits a boundary or ___________________, some
energy is __________________ forward, and the rest is
__________________ backward. If the next pulse is produced at
just the right time, we can get both waves (incoming and reflected)
to constructively interfere at the same points and destructively
interfere at points between. This produces a ______________
________. The points of large amplitude are called
____________, while the points of no amplitude are called
___________.
A standing wave with one anti-node would look like this:
A standing wave with two anti-nodes would look like this:
A standing wave with three anti-nodes would look like this:
If the one anti-node picture was produced by a frequency of 15 Hz,
what frequencies would produce the two and three anti-node
pictures?
The Doppler Effect
If a source is producing sound waves, they will spread out in
______ _______________. The f________________ of the
sound will be the same both in front of and behind the source.
A picture of a non-moving source looks like this:
Now, if the source begins to move, in front of the source, the
____________________ shrinks, and so the __________________
increases. Now the sound is perceived as ____________ than it
originally was produced.
Behind the source, the converse is true. The wavelength will
________________ and so frequency will ________________.
The sound will be perceived as ________________ than it
originally was produced.
A picture of a moving source looks like this:
This phenomenon of a moving source causing a ____________
frequency in front of the source and a __________ frequency
behind the source is called the ______________ ____________.
The Doppler Effect occurs for ______ waves, even light. When a
light source, like a ________ moves away from you, the light’s
__________________ will be _____________ than it should be,
that is shifted toward the ________ end of the spectrum. This is
called a __________ ___________.
The reverse is true when the light moves toward you. Then the
frequency will be ____________ than it should be, and will look
closer to the ______ end of the spectrum. This is called a _____
_________.
Bow Waves & Shock Waves
Bow waves take the Doppler Effect to the extreme. When the
speed of a source ____________ the speed of a wave, the waves
cannot gain any _______________ on the source. Now, the waves
will all be ____________ the source, like this:
This resulting V-Shape is called a ________ _________.
In a bow wave, we will get a large __________________ on the V
itself. This results from crests overlapping on ____________
producing _____________________ ______________________.
Planes do the same thing three-dimensionally in the air. Normally,
sound waves travel in front and behind the plane. However, a
plane which can travel faster than the speed of sound
(____________________) will have all its sound behind it in a
________ shape. This cone is called a __________
___________. At the edges, we get large constructive
interference, and consequently, large ________________. A
person on the ground would not be able to hear this plane until
after it has passed, as you can see:
When the cone does contact the person, the loud sound they hear is
a __________ ____________. Many non-physics types think this
occurs only when
_______________________________________
________________________________, but it occurs
___________________, as long as the plane stays above the speed
of _______________________.
Vibration
Time
Cute
Over and over
Distance
Waves
Travel away
Vibrations
Galileo
Heartbeat
Period
T
Length
Mass
Period
Non-physics type
T = 2π √(L/g)
Curve
Square root
Variable
Constant x variable
Constant
Amplitude
Sine wave
Vibrating source
Wave
Energy
Pulse
pulses
timed
spaced out
medium
cause
disturbance (energy)
particles
interact
equilibrium
energy
crests
maximum
negative
troughs
Amplitude
Equilibrium
THE
Changes
Given
Time
Wavelength
Full waveshape
λ
frequency
number
waves
time interval
Hertz (Hz)
f = # waves/time
interval
f = 2 waves/1 second
f = 2 waves/second = 2
Hz
reciprocals
0.5 seconds
Particle
Agent
Baseball, tree branch,
flying acrobat
Wave
Medium
Light, water waves,
slinky waves, sound
Vibrate
Same place
Started
Amplitude
Amplitude
Work
9 times
3 times
direct square
υ
medium
deep
shallow
tension
distance/time
wavelength/period
wavelength x frequency
7.5 m/s
wave speed
it will double
Transverse
longitudinal
surface
circles
breaks
influence
work
solids
fluids
fluids
compressions
rarefactions
collisions
solids
fluids
simultaneously
medium particles
constructive
in-phase
or
destructive
out-of-phase
interface
transmitted
reflected
standing wave
anti-nodes
nodes
(see above)
sonic boom
the plane first goes
faster than the speed of
sound
continually
sound
higher
lower
Doppler Effect
All
Star
Frequency
Lower
Red
Red shift
Higher
Blue
Blue shift
Matches (equals)
Distance
Behind
30 Hz
45 Hz
all directions
frequency
wavelength
frequency
higher in pitch
get bigger
get smaller
lower in pitch
bow wave
amplitude
crests
constructive interference
supersonic
cone
shock wave
amplitude (volume)