Transcript Vibrations and Waves. So much fun, you can’t stand it!

Vibrations and Waves.
So much fun, you
can’t stand it!
First rule of leadership: everything is
your fault.
She wrote me a 'john-deere' letter... something about
me not listening enough, I don't know... I wasn't really
paying attention.
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Take a pendulum, guitar string, weight
bobbing on a spring, all of these objects
have a motion that repeats in cycles, and
all are examples of periodic motion.
If the force that restores the object to its
equilibrium position is directly proportional
to the displacement of the object is it in
simple harmonic motion.
Our generation has had no Great Depression, no Great
War. Our war is spiritual. Our depression is our lives.
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Two properties describe something that is
in simple harmonic motion, period and
amplitude.
Period, is the time it takes for one
complete cycle of a wave or periodic
motion.
Amplitude, is the greatest displacement
from rest
I'm going to make him an offer he
can't refuse.
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Springs can exhibit periodic motion
because the force exerted by the spring is
directly proportional to the distance it is
stretched multiplied by a spring constant
specific to the type of spring.
This is known as Hooke’s Law F=-kx
F = force, k = spring constant, x = distance
You've got to ask yourself one question: 'Do I feel
lucky?'
Well, do ya, punk?
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Most springs obey this law, but not all.
If I graph Force versus distance with regard
to a spring the slope of the graph is equal
to the spring constant and the area under
the graph is equal to the work done by the
spring.
Potential energy in a spring is equal to
PE = ½ kx2
You had me at "hello."
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The period of oscillation of a spring
depends on the mass of the object and the
strength of the spring. T = 2
The period of a pendulum is a function of
the length of the rod or string and gravity
and looks like this:
T=2
l/g
There's no crying in baseball!
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Resonance, occurs when small forces are applied
at regular intervals to a vibrating or oscillating
object and the amplitude or vibration increases
The addition of small forces at specific times
increases the amplitude
Pushing a stuck car, trampoline, diving board etc.
Resonance can be very destructive to structures.
Say "hello" to my little friend!
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A wave is a disturbance that carries energy
through matter or space. It does not carry
matter.
Mechanical waves are waves that need a
medium to travel.
Electromagnetic waves do not.
Here's Johnny!
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There are 3 types of mechanical waves.
Transverse waves displace matter
perpendicular to the direction of wave
motion. (think rope, sine curve, etc)
Longitudinal (compressional) waves
displace matter parallel or inline with the
direction of the wave. ( Think slinky,
earthquake)
I feel the need -- the need for speed!
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Surface waves, aka water waves are a
combination of both transverse and
longitudinal.
Water particles are displaced both
perpendicular and longitudinal to the wave
direction
Did they teach you how to apologize
at lawyer school? 'Cause you suck at it
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Wave properties include speed, amplitude,
crest, trough, wavelength, frequency,
period, phase.
Speed is a function of delta d/ delta t
Amplitude is the greatest displacement
from rest, greater amplitude, greater
energy.
Real loss is only possible when you love
something more than you love yourself.
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Energy transferred is equal to the
amplitude squared.
For waves at the same speed, doubling the
amplitude increases the amount of energy
it transfers by a factor of 4
Crest is the high point of the wave
Trough is the low point
Give me some sugar, baby!
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In a longitudinal wave, compression and
rarefaction are synonymous with crest and
trough.
Wavelength is equal to one complete wave
cycle or any two equal points on the wave,
crest to crest, trough to trough.
Represented by the Greek letter lambda
I see dead people.
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Frequency is the number of complete oscillations
per second and is also the inverse of the period of
the wave.
f = 1/T
Frequency is measureed in hertz, 1 cycle/second
Wavelength is equal to velocity divided by
frequency Wavelength = v/f
Phase is one waves relation to another
If I'm not back in five minutes... wait
longer!
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The speed of a wave depends on the
medium it travels through, not the
amplitude or frequency. Sound waves for
example travel slower in colder air than
warm air, light travels slower through glass
than through air.
When waves strike a barrier the incoming
wave is the incident wave the outgoing
wave is the reflected wave.
Super Long Slinky in the Hall
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The reflected wave off of a more dense
object will be the inverse, same magnitude.
The reflected wave off of something less
dense will the same phase but with less
magnitude, the rest of the wave is carried in
onto the other medium.
Seems to me, Cap'n, this mission is a
serious misallocation of valuable military
resources.
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The principle of superposition states that the
displacement of a medium by two or more waves
is the algebraic sum of the displacement of the
individual waves.
Waves can either have constructive interference
or destructive interference.
When waves cancel and result in no
displacement, this is called a node.
When waves build and result in increased
displacement this is called an antinode.
“I’ll be your huckleberry”
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A standing wave is one that appears to be
still with nodes at one end and the antinode
in the middle. Doubling the frequency
produces one more node and antinode.
I didn’t get this job by being in the 75th
percentile
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When waves reflect off of a boundary the angle of
incidence equals the angle of reflection from the
normal (an imaginary line drawn perpendicular
from the boundary)
Refraction is the bending or slowing of a wave as
it passes from one medium to another.
A wave front represents the crest of a wave in two
dimensions