Transcript How do we describe simple harmonic motion?

HOW DO WE DESCRIBE
SIMPLE HARMONIC MOTION?
Why learn about waves?
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Waves carry useful
information and energy.
Waves are all around us:
 light
from the stoplight
 ripples in a puddle of
 electricity flowing in wires
 radio and television and cell
phone transmissions
Characteristics of waves
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Waves have cycles, frequency, and amplitude, just like
oscillations.
The frequency of a wave tells
how often each point oscillates.
The wavelength of a wave is the
length of one complete cycle.
The amplitude of a wave is the
maximum movement from
equilibrium.
Periodic Motion
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A motion of an object that repeats with a constant
period.
http://www.sccs.swarthmore.edu/users/08/ajb/e71/lab1/
Simple Harmonic Motion
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It is a periodic motion.
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AND
It has a restoring force that acts to restore the oscillator
to equilibrium. The restoring force is given by:
Hooke’s Law F=-kx
x is the displacement from equilibrium
and k is the force constant
(spring constant).
Describing Waves
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A vibration of a system in which some particular points remain fixed
while others between them vibrate with the maximum amplitude.
Standing waves have nodes and antinodes.
A node is a point where the string stays at its equilibrium position.
An antinode is a point where the wave is as far as it gets from
equilibrium.
Guitar string & standing wave
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/sound/soundtoc.html
Why Things Oscillate
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Systems that have harmonic motion
move back and forth around a central
or equilibrium position.
Equilibrium is maintained by restoring
forces.
A restoring force is any force that
always acts to pull the system back
toward equilibrium.
Harmonic Motion is Common
sound
communications
clocks
nature
Position VS. Time graph
Amplitude
•Amplitude is the magnitude of the maximum displacement.
• For any object in simple harmonic motion, the time required to
complete one cycle is the period T.
Frequency, f
The frequency f of the simple harmonic motion is the
number of cycles of the motion per second.
Measured in Hertz (1/s) Hz
f = 1/T
Inertia
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Newton’s first law explains why harmonic motion happens for
moving objects.
According to the first law, an object in motion stays in motion
unless acted upon by a force.
Relationship between speed, frequency,
and wavelength
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The speed of a wave equals the frequency times
the wavelength.
Frequency (cycles/sec)
Speed (m/sec)
v=fλ
Wavelength (m)
What does the period depend on?
Length of the pendulum (l).
Acceleration due to gravity (g).
Period does not depend upon
the bob mass or the amplitude
of the swing.
T 2 l g
Vibration of a pendulum.
The to-and-fro vibratory
motion is also called
oscillatory motion (or
oscillation).
Transverse and Longitudinal Waves
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A transverse wave has its oscillations perpendicular
to the direction the wave moves.
 A longitudinal wave has oscillations in the same
direction as the wave moves.
Interference
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If two waves add up to create a larger amplitude, constructive
interference has occurred.
In destructive interference, waves add up to make a smaller
amplitude.
Natural Frequency and Resonance
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Waves can show natural frequency and
resonance, just like oscillators.
The natural frequency of a wave depends on
the wave and also on the system that contains
the wave.
Resonance in waves is caused by reflections
from the boundaries of a system.
How is a Sonic Boom created?
What Makes a Light Wave Different
than a Sound Wave?
•
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•
Light travels a million times faster than
sound:
Speed of light in air = 300,000,000 meters
per second
Speed of sound in air (at 0 Celsius) = 331
meters per second.
•
Light can travel in empty space
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…Sound can’t because sound is the
compression of the medium
Transverse vs. Longitudinal
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Light is a transverse wave:
Transverse means that the wave travels perpendicular to the displacement
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Sound is a longitudinal wave
The wave travels in the same direction as the displacement
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Light gets slower in denser objects
(Faster: air, water, glass :Slower)
Sound gets faster in denser objects
(Slower: gas, liquid, solid :Faster)
Doppler Effect
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The Doppler effect can be described as the effect
produced by a moving source of waves in which
there is an apparent upward shift in frequency for
the observer and the source are approaching and
an apparent downward shift in frequency when the
observer and the source is receding.
http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/sound/soundtoc.html
http://cse.ssl.berkeley.edu/bmendez/ay10/2002/notes/pics/bt2lf0615_a.jpg
What is the Electromagnetic Spectrum?