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Physics
Coach Kelsoe
Pages 366-395
Section 1-Simple Harmonic Motion
Objectives:
 Identify the conditions of simple harmonic motion
 Explain how force, velocity, and acceleration change as
an object vibrates with simple harmonic motion
 Calculate the spring force using Hooke’s Law
Intro to Hooke’s Law
 At the equilibrium
position, speed reaches a
maximum
 At maximum
displacement, spring force
and acceleration reach a
maximum
 In simple harmonic
motion, restoring force
is proportional to
displacement
Simple Harmonic Motion
 Simple harmonic motion-vibration about an
equilibrium position in which a restoring force is
proportional to the displacement from
equilibrium
Putting it in perspective…
 Think of a pendulum on a clock for
example.
 As the pendulum swings outward it
reaches its maximum displacement.
 The pendulum’s starting position is
its equilibrium. Therefore as the
pendulum swings it constantly
moves in simple harmonic motion,
constantly moving from its
maximum displacement to its
equilibrium.
Hooke
 Hooke’s law is the relationship between the restoring
force and the displacement of the mass.
 Easily written as…
Felastic= -kx
spring force= - (spring constant x displacement)
Negative sign signifies that the direction of the
spring force is always opposite the direction of the
mass’s displacement from equilibrium.
The Simple Pendulum
 The restoring force of a pendulum is a component of
the bob’s weight
 For small angles, the pendulum’s motion is simple
harmonic
 Gravitational potential increases as a pendulum’s
displacement increases
Section 2-Measuring Simple
Harmonic Motion
Objectives:
 Identify the amplitude of vibration
 Recognize the relationship between period and
frequency
 Calculate the period and frequency of an object
vibrating with simple harmonic motion
Amplitude, Period, and Frequency
 Amplitude- the maximum displacement from
equilibrium (radians or meters)
 Period (T)-the time that it takes a complete cycle
to occur (seconds)
 Frequency (f)-the number of cycles or vibrations
per unit of time (Hertz-Hz)
 Frequency is the inverse of period.
 The period of a simple pendulum depends on
pendulum length and free-fall acceleration.
T=2π √L/ag
 Mass does not affect acceleration so therefore the
pendulums’ period is the same.
 Have you ever noticed that when you first watch a
pendulum it moves its maximum displacement when
it first takes off? This is because when the amplitude
increases the restoring force increases proportionally.
 Force is proportional to acceleration, so the initial
acceleration will be greater.
 Period of a mass-spring system depends on mass and
spring constant.
 Period of a mass-spring system in simple harmonic
motion:
T=2π√m/k
(period=2π/square root of (mass
divided by spring constant)
Section 3-Properties of Waves
Objectives:
 Interpret waveforms of transverse and longitudinal
waves.
 Apply the relationship among wave speed, frequency,
and wavelength to solve problems.
Transverse vs. Longitudinal
 There are two types of waves: transverse and
longitudinal.
 Transverse waves are perpendicular to the wave
motion.
 Longitudinal waves are parallel to the wave
motion.
 Waves can be measured in terms of its
displacement.
Important Definitions:
 Transverse wave- a wave whose particles vibrate
perpendicularly to the direction the wave is
traveling.
 Crest-the highest point above the equilibrium
position
 Trough- the lowest point below the equilibrium
position
 Wavelength-distance between two adjacent
similar points of a wave, such as from crest to
crest or from trough to through
 Longitudinal wave- wave whose particles vibrate
parallel to the direction the wave is traveling
…
 Medium- a physical environment through which a
disturbance can travel
 Mechanical wave- a wave that requires a medium
through which to travel
Finding speed of wave
 After deriving, the speed of the wave is equal to
frequency times wavelength…

V=f λ
Section 4- Wave Interactions
 Constructive Interference- a superposition of two
or more waves in which individual displacements
on the same side of the equilibrium position are
added together to form the resultant wave
 Destructive Interference- a superposition of two
or more waves in which individual displacements
on opposite sides of the equilibrium position are
added together to form the resultant wave.
 Standing Wave-a wave pattern that results when
two waves are the same frequency, wavelength,
and amplitude travel in opposite directions and
interfere.
Continues with…
 Node- a point in a standing wave that maintains
zero displacement
 Antinode- a point in a standing wave, halfway
between two nodes, at which the largest
displacement occurs.
Just a few things to know…
 If two or more waves are moving through a
medium, the resultant wave is found by adding
the individual displacements together point by
point.
 Standing waves are formed when two waves that
have the same frequency, amplitude, and
wavelength travel in opposite directions and
interfere.
Chapter 12
Sound
Sound
Physics
Compression is the region of a longitudinal wave in
which the density and pressure are at a maximum.
Rarefaction is the region of a longitudinal wave in which
the density and pressure are at a minimum.
Pitch is a measure of how high or low a sound is perceived
to be, depending on the frequency of the sound wave.
The Doppler Effect is an observed change in frequency
when there is relative motion between the source of waves
and an observer.
Characteristics of Sound Waves
 Frequency determines pitch. The frequency of an audible
sound wave determines how high or low we perceive the
sound to be, which is known as pitch. As the frequency of a
sound wave increases, the pitch rises.
 The speed of sound depends on the medium. Because
waves consist of particle vibrations, the speed of a wave
depends on how quickly one particle can transfer its
motion to another particle. The speed also depends on the
temperature of the medium.
 Sound waves
propagate in three
dimensions. Sound
waves travel away
from a vibrating
source in all three
dimensions. The
wave fronts of
sound waves
spreading in three
dimensions are
approximately
spherical.
Rarefaction and Compression
Example of Refraction and
Compression
 The sound from a tuning fork is produced
by the vibrations of each of its prongs.
 When a prong swings to the right, there is
a region of high density and pressure.
 When the prong swings back to the left, a
region of lower density and pressure
exists.
Doppler Effect!
As a police car or ambulance
passes you, with its siren
wailing, the sound of the siren
seems to drop to a lower note.
This is due to something
known as the Doppler Effect,
named after the Austrian
scientist Christian Johann
Doppler, who discovered the
reason for it in 1842.
The Doppler Effect is defined
as an observed change in
frequency when there is
relative motion between the
source of waves and an
observer.
Doppler found that if a source of
sound is moving, the sound waves
are crowded together in front of it
and spread apart behind it.
Squeezing sound waves together
increases their frequency, while
spreading them lowers their
frequency. As a result, to someone
at rest the sound will seem higher
when the source is approaching
and lower when it is moving away.
At the time when Doppler announced his findings, there was no easy means to test
them. The fastest form of transport which carried a horn was the horse-drawn mail
coach. This only moved at about ten miles an hour – too slow for the Doppler
Effect to be noticeable. It was only in 1845, when a scientist took a trumpet aboard
a train locomotive, that the effect was first demonstrated.
Sound Waves
Section Two Vocabulary
 Intensity is the rate at which energy flows through a
unit area perpendicular to the direction of wave
motion.
 A decibel (dB) is a dimensionless unit that describes
the ratio of two intensities of sound; the threshold of
hearing is commonly used as the reference intensity
 Resonance is a phenomenon that occurs when the
frequency of a force applied to a system matches the
natural frequency of vibration of the system, resulting
in a large amplitude of vibration
Sound Intensity!
 Intensity is the rate of energy flow through a
given area.
 Sound waves traveling in air are longitudinal waves. As the sound waves
travel outward from the source, energy is transferred from one air
molecule to the next. The rate at which this energy is transferred
through a unit area of the plane wave is called the intensity of the
wave.
 Because power, P, is defined as the rate of energy transfer, intensity can
also be described in terms of power. Intensity has units of watts
per square meter (W/m₂)
 Intensity= ΔE/ Δt =
area
P
area
Intensity of a Spherical Wave
In a spherical wave, energy propagates equally in all
directions; no one direction is preferred over any other.
The power emitted by the source (P) is distributed over a
spherical surface (area=4∏r₂), assuming that there is
no absorption in the medium.
• Intensity =
(power)
.
(4∏)(distance from the source)₂
Decibels and Sound
Moderation
 Intensity and frequency determine which sounds are
audible.
 The softest sound that can be heard by the average
human ear occurs at a frequency of about 1000 Hz and an
intensity of 1.0 x 10-12. Such a sound is said to be at the
threshold of hearing.
 The loudest sounds that the human ear can tolerate have
an intensity of about 1.0 W/m2. This is known as the
threshold of pain.
 Relative intensity is measured in decibels.
 Relative intensity is the ratio of the intensity of a given
sound wave to the intensity at the threshold of
hearing.
 Because of the logarithmic dependence of perceived
loudness on intensity, using a number equal to 10
times the logarithm of the relative intensity provides a
good indicator for human perceptions of loudness.
 This is referred to as the decibel level.
 The decibel level is dimensionless because it is
proportional the logarithm of a ratio.
Forced Vibrations and Resonance
 Vibrations at the natural frequency produces
resonance.
 Every pendulum vibrates at a certain frequency known
as its natural frequency.
 The human ear transmits vibrations that cause
nerve impulses.
 Sound waves travel through the three regions of the
ear and are then transmitted to the brain as impulses
through nerve endings on the basilar membrane.
Sound waves of varying
frequencies resonate at
different spots along the
basilar membrane, creating
impulses in hair cells
embedded in the membrane.
These impulses are then
sent to the brain, which
interprets them as sounds of
varying frequencies.
Section Three Vocabulary
 Fundamental frequency is the lowest frequency of
vibration of a standing wave.
 A harmonic series is a series of frequencies that includes
the fundamental frequency and integral multiples of the
fundamental frequency.
 Timbre is the musical quality of a tone resulting from
the combination of harmonics present at different
intensities.
 A beat is the periodic variation in the amplitude of a
wave that is the superposition of two waves of slightly
different frequencies.
Standing Waves on a Vibrating
String
The vibrating strings of a violin
produce standing waves whose
frequencies depend on the string
lengths.
Wave Basics
•High points of the wave are called Crests
•Low points are troughs
•Amplitude is the maximum
displacement from the
undisturbed state.
•Can be positive or negative.
•The Wavelength is the distance between two adjacent
corresponding points on the wave.
•A waves frequency refers to how many waves are made per
time interval, usually in seconds.
 The Doppler effect (or Doppler shift), named after
Austrian physicist Christian Doppler who proposed it
in 1842
 The Doppler effect is how wave properties, specifically
frequencies, are influenced by the movement of the source
and the listen.
 The most common examples of this would be a train
passing or police sirens.
 The frequency of the sounds that the source emits
does not actually change. Merely the wavelength and
the received are affected.
 The sounds are being sent out at the same rate but the
person moving towards or away from the source hear
them at changing intervals.
 To calculate the change in frequency due to the Doppler
effect, consider a situation where the motion is set
between a Listener L and the source S with the direction
from listener to the source as the positive direction.
 fL = [(v + vL)/(v + vS)] fS
 The velocities vL and vS are the velocities of the listener and
source relative to the wave medium. The speed of the
sound wave, v, is always considered positive.
 After figuring all that out we get the frequency heard by the
listener (fL) in terms of the frequency of the source (fS):
 If the listener is at rest vL = 0.
 If the source is at rest vS = 0.
 That means if both the listener and the source are at rest
fL = fS.
 If the listener is moving toward the source, then vL > 0,
though if it's moving away from the source then vL < 0.
 Alternately, if the source is moving toward the listener the
motion is in the negative direction, so vS < 0, but if the
source is moving away from the listener then vS > 0.
The Doppler Effect in Light
 The major difference between light waves and sound waves
is that light waves do not require a medium to travel
through.
 Light waves from a moving source experience the Doppler
effect to result in either as a red shift or blue shift in the
light's frequency.
 A “Blue shift” occurs when the wavelength of light
decreases and or the frequency increases.
 A “Red Shift” happens when a star or other object is moving
away from the observer.