Download Introduction to Waves

3/23 do now – on a new sheet
1. What are the four factors that affect resistance?
2. A student conducted an experiment to determine the
resistance of a light bulb. As she applied various
potential differences to the bulb, she recorded the
voltages and corresponding currents. The student
noticed that the light bulb began to glow and became
brighter as she increased the voltage. Of the factors
affecting resistance, which factor caused the greatest
change in the resistance of the bulb during her
experiment?
Introduction to Waves - Chapter
Outline
Lesson 1: Vibrations
Lesson 2: The Nature of a Wave
Lesson 3: Properties of a Wave
Homework: castle learning
Period 8 – electricity unit exam part I is on castle learning
Lesson 1: Vibrations
1. Vibrational Motion
2. Properties of periodic Motion
3. Pendulum Motion
Vibrational Motion
A vibrational motion is a back and forth motion.
All vibrational motion has
•
•
•
•
•
Resting position or equilibrium position. At this position, the
forces are balanced.
To make an object vibrate, a force must be applied to the object.
The object does not stop at equilibrium position because of
inertia.
As the object reaches its maximum displacement, it stops
momentarily before it moves back. This is because the object
experiences a force which slows it down. This force is known as
a restoring force.
Damping is the tendency of a vibrating object to lose its energy
over time. A sustained input of energy would be required to keep
the back and forth motion going.
Properties of Periodic Motion
• A vibrating object is moving over the same
path over the course of time.
• The time it takes to complete one back and
forth cycle is always the same amount of time.
• In Physics, a motion that is regular and
repeating is referred to as a periodic motion.
The Sinusoidal Nature of a Vibration
• The position vs. time graph of mass on a spring:
1. The graph has the shape of a sine wave - periodic. The motion
repeats itself in a regular fashion.
2. The time to complete one cycle of vibration is NOT changing.
3. Damping occurs with the mass-spring system, the amount of
displacement of the mass at its maximum and minimum height is
decreasing from one cycle to the next.
Amplitude, period and frequency
• AMPLITUDE (A): the maximum displacement from
equilibrium. It is a reflection of ENERGY possessed
by the vibrating object. The SI unit of A is m, cm, …
• PERIOD (T): the TIME it takes to execute ONE COMPLETE
CYCLE of motion. The SI unit of T is second.
• FREQUENCY (f): the NUMBER OF CYCLES or vibrations
PER UNIT OF TIME. The SI unit of f is Hertz or (1/s)
Amplitude, Period, Frequency
Examples
• Amplitude: 0.01 m
• Period (T) is 0.05 s (time of one complete cycle)
• Frequency (f) describes number of cycles per unit of time:
• f = 2/0.10s = 20 Hz.
Amplitude Represents Energy
• The amplitude is defined as the maximum displacement of an
object from its resting position. The resting position is that
position assumed by the object when not vibrating.
• Over the course of time, the amplitude of a vibrating object
tends to become less and less. The amplitude of motion is a
reflection of the quantity of energy possessed by the vibrating
object.
Period And Frequency Are Inversely Related
• Objects that have a relatively short period (i.e., a low value for
period) are said to have a high frequency.
1
T
f
Check Your Understanding
1.
A pendulum is observed to complete 23 full cycles in 58
seconds. Determine the period and the frequency of the
pendulum.
frequency = 23 cycles/58 seconds = 0.39655 Hz = ~0.40 Hz
period = 58 seconds/23 cycles = 2.5217 sec = ~2.5 s
2.
A mass is tied to a spring and begins vibrating periodically.
The distance between its highest and its lowest position is 38
cm. What is the amplitude of the vibrations?
19 cm
Pendulum Motion is Periodic
•
•
•
FTen
•
Fnet
Fgrav
A simple pendulum consists a bob
(mass) attached to a string of
negligible mass.
The two force acting on the bob are
gravity and tension force.
The gravity is always in the same
direction (down) and always of the
same magnitude - m∙g. However, both
the direction and magnitude of the
tension force change as the bob swings
to and fro.
The net force is the restoring force
which causes the pendulum’s periodic
motion.
Energy Analysis of a Pendulum
• As the bob of a pendulum moves from one end to the other
end, there is a transformation of potential energy into kinetic
energy and vise versa. However, the total amount of these two
forms of energy, the total mechanical energy remains
constant.
Check Your Understanding
1. A pendulum bob is pulled back to position A and released from rest.
The bob swings through its usual circular. Determine the position
(A, B, C or all the same) where the …
a. force of gravity is the greatest.
same
b. restoring force is the greatest.
A
c. speed is the greatest.
d. potential energy is the greatest
A,C
e. kinetic energy is the greatest.
f. total mechanical energy is the greatest.
same
2. Use energy conservation to fill in the
blanks in the following diagram.
The Period of a Pendulum
• The period is the time it takes for a vibrating object to
complete one cycle. In the case of pendulum, it is the
time for the pendulum to start at one extreme, travel
to the opposite extreme, and then return to the
original location.
• variables that might affect the period of a pendulum:
– the mass of the pendulum bob,
– the length of the string on which it hangs,
– and the angular displacement (amplitude). The
angular displacement or arc angle is the angle that
the string makes with the vertical when released
from rest.
The period of pendulum
• For amplitude that less than 15o, the period of a simple
pendulum is independent of mass and amplitude
(angle).
• the period is directly proportional to the square root of
the length of the string.
l
T  2
g
• Where l is the length of the string in meters, T is the
period in seconds, g = 9.81 m/s2
graphs
Period vs. √length
period
period
Period vs. length
Length (m)
√Length (m)
example
• You need to know the height of a tower, but darkness
obscures the ceiling. You note that a pendulum
extending from the ceiling almost touches the floor and
that its period is 12 s. how tall is the tower?
Given:
Solve:
T = 12 s
T = 2π√l/g
g = 9.81 m/s2
l = 36 m
Unknown:
l=?
Example
•
A pendulum is timed as it moves from its starting point “A” to
several other positions as it swings.
a.
Use the data from the position/time chart to determine the period
of the pendulum. _________s
Calculate the frequency of the pendulum.
Use the period of the pendulum to calculate the length of the
pendulum string.
b.
c.
3/24 do now
• A piece of coper wire with a crosssectional area of 3.0 x 10-5 m2 is 25 m
long. How would changing the length of a
copper wire change its resistivity?
A.Resistivity will increase.
Explain your
B.Resistivity will decrease.
answer
C.Resistivity will not change.
homework: castle learning
Pd. 8 – electricity unit exam part I on castle
learning will close tonight
Lesson 2 - The Nature of a Wave
1. What is a Wave?
2. Distinguish local particle vibrations from overall wave
motion.
3. Wave transfers energy only and energy is related to the
amplitude.
4. Differentiate between pulse waves and periodic waves.
5. Interpret waveforms of transverse and longitudinal
waves
6. Categories of Waves
What is a wave?
• A WAVE is the motion of disturbance. Some
disturbance can only go through a medium,
others can go through both a medium or vacuum
(empty space).
• A MEDIUM is a body of matter, such as water,
air, people, slinky, etc.
All waves are produced by a vibrating SOURCE.
A wave is started with a vibration and its frequency is the same
as its source. The vibration travels from one location to another.
Sound wave is produced by a vibrating vocal cord.
Radio waves is produced by accelerating electrons in a transmitter.
example
•
1.
2.
3.
4.
The diagram shows an antenna emitting an
electromagnetic wave. In what way did the electrons in
the antenna produce the electromagnetic wave?
by remaining stationary
by moving at a constant speed upward, only
by moving at a constant speed downward, only
by accelerating alternately upward and downward
example
•
1.
2.
3.
4.
How are electromagnetic waves that are produced by
oscillating charges and sound waves that are produced
by oscillating tuning forks similar?
Both have the same frequency as their respective
sources.
Both require a matter medium for propagation.
Both are longitudinal waves.
Both are transverse waves.
Waves and energy transfer
• Wave can transfer ENERGY from one place to another
– Either through vibrations of particles in a medium,
– Or by repeated small changes in the strength of a
field.
• The source provides the initial vibrations, but there is NO
ACTUAL TRANSFER OF MASS from the source.
• ONLY ENERGY is transferred from the source.
A wave has a crest and a trough
crest
trough
• The size of crest or trough determines the amount of
energy in a wave
.
example
•
1.
2.
3.
4.
A characteristic common to sound waves
and light waves is that they
are longitudinal
are transverse
transfer energy
travel in a vacuum
Check Your Understanding
1. TRUE or FALSE:
In order for John to hear Jill, air molecules must move from
the lips of Jill to the ears of John.
2. Curly and Moe are conducting a wave experiment using a
slinky. Curly introduces a disturbance into the slinky by giving
it a quick back and forth jerk. Moe places his cheek (facial) at
the opposite end of the slinky. Using the terminology of this
unit, describe what Moe experiences as the pulse reaches the
other end of the slinky.
Moe experiences a pulse of energy
Local Particle Vibrations And Overall Wave Motion.
The wave is passed from left to
right from one side to another, but
the local particle does not move
from one side to another, local
particles vibrates locally
What is the direction of motion in the medium?
v
v
As the wave travels to right or left, a single point in the
medium will only moves UP or DOWN, IN THE SAME
DIRECTION AS THE POINT BEFORE IT.
Example #1
•
a.
b.
c.
d.
As shown in the diagram, a pulse is moving
along a rope. In which direction will segment X
move as the wave passes through it?
down, only
up, only
down, then up
up, then down
Example #2
•
The diagram shows a pulse moving in the
direction shown by velocity vector v. At the
instant shown, a cork at point P on the water's
surface is moving toward
a.
b.
c.
d.
A
B
C
D
Example
#3
v
•
In the next instant of time, indicate
a. The direction of motion of point A.
b. The direction of motion of point B.
c.
The direction of motion of point C.
d. The direction of motion of point D.
Example #4
•
The diagram below represents a transverse
wave traveling to the right through a medium.
Point A represents a particle of the medium. In
which direction will particle A move in the next
instant of time?
A Pulses vs. Periodic Waves
• A wave may be classified as either a pulse or a periodic
wave.
• A PULSE is a SINGLE vibratory disturbance that transfers
energy but NOT mass.
• A WAVE is a PERIODIC vibratory disturbance that transfers
energy but NOT mass.
TRANSVERSE waves vs. LONGITUDINAL waves
Transverse Wave – particles of the medium move
PERPENDICULAR to the wave’s direction of travel
Longitudinal Wave – particles of the medium move PARALLEL
to the wave’s direction of travel.
Examples of Longitudinal and transverse
wave
• Transverse:
–
–
–
–
http://www.suu.edu/faculty/colberg/Ha
Wave on a string
zards/Earthquakes/31_surface_waves_
Stadium wave
earthquakes/31.html
Wave on a slinky
ELECTROMAGNETIC WAVES (light, RADIO,
microwaves, UV rays, etc)
• Longitudinal:
– SOUND WAVE
– Wave on slinky
– Earthquake
Electromagnetic versus Mechanical Waves
• Another way to categorize waves is on the basis of their ability to
transmit energy through a vacuum (i.e., empty space).
• An electromagnetic wave, such as radio wave, which are
produced by the vibration of charged particles, is a wave which
is capable of transmitting its energy through a vacuum (i.e.,
empty space).
• A mechanical wave is a wave which is not capable of
transmitting its energy through a vacuum. Mechanical waves
require a medium in order to transport their energy from one
location to another.
• A sound wave is an example of a mechanical and longitudinal
wave. Sound waves are incapable of traveling through a vacuum
A summary of categories of waves
• Category by direction:
– Transverse (wave on a string, ocean wave, stadium wave)
– Longitudinal (sound wave, slinky wave)
• Category by medium
– Electromagnetic (light)
– Mechanical (all other waves)
• There are other categories as well.
• Light waves are electromagnetic and transverse
waves.
• Sound waves are mechanical and longitudinal
waves.
3/25 do now
• Circuit A has four 3.0-ohm resistors connected
in series with a 24-volt battery, and circuit B has
two 3.0-ohm resistors connected in series with a
24-volt battery. Compared to the total potential
drop across circuit A, the total potential drop
across circuit B is
1. one-half as great
2. twice as great
Explain your answer
3. the same
4. four times as great
Example
•
1.
2.
3.
4.
A student plucks a guitar string and the vibrations
produce a sound wave with a frequency of 650 hertz.
The sound wave produced can best be described as a
transverse wave of constant amplitude
longitudinal wave of constant frequency
mechanical wave of varying frequency
electromagnetic wave of varying wavelengths
Example
•
1.
2.
3.
4.
An electric bell connected to a battery is sealed inside a
large jar. What happens as the air is removed from the
jar?
The electric circuit stops working because
electromagnetic radiation cannot travel through a
vacuum.
The bell's pitch decreases because the frequency of the
sound waves is lower in a vacuum than in air.
The bell's loudness increases because of decreased air
resistance.
The bell's loudness decreases because sound waves
cannot travel through a vacuum.
Example
•
1.
2.
3.
4.
Which pair of terms best describes light waves
traveling from the Sun to Earth?
electromagnetic and transverse
electromagnetic and longitudinal
mechanical and transverse
mechanical and longitudinal
Lesson 3 - Properties of Waves
objectives
• The Anatomy of a Wave - Crest, Trough,
Compression, Rarefaction, Frequency,
Period, Wavelength, Amplitude of a Wave
• Energy Transport and the Amplitude of a
Wave
• The Speed of a Wave
• The Wave Equation
The Anatomy of a transverse wave
Transverse Wave – particles of the medium move
PERPENDICULAR to the wave’s direction of travel
v
crest
wavelength (λ)
A
amplitude
trough
Motion of
particles in
the medium
TRANSVERSE WAVE
Crest, trough, A, λ, T, f
• CREST: the highest point in a waveform.
• TROUGH: the lowest point in a waveform
• AMPLITUDE (A): maximum displacement of a particle on the
medium from its rest (equilibrium) position. From rest to crest or
from the rest to trough. The amount of ENERGY carried by a
wave is related to the amplitude of the wave. A high energy wave
is characterized by a high amplitude; a low energy wave is
characterized by a low amplitude.
• WAVELENGTH (λ): length (distance) of one complete wave
cycle. It can be measured as the distance from a point on a wave
to the corresponding point on the next cycle of the wave
• PERIOD (T): time of once complete wave cycle. It is measured
in unit of time (sec, min, hr…)
• FREQUENCY (f): number of cycles per unit of time. (1/T)
The Anatomy of a longitudinal wave
Longitudinal Wave – particles of the medium move PARALLEL to
the wave’s direction of travel.
v
SOUND WAVES
Faster in DENSE mediums
wavelength (λ)
compression
rarefaction
Motion of
particles in the
medium
LONGITUDINAL WAVE
Compression, Rarefaction, A, λ, T, f
• COMPRESSION: the most compressed part in a waveform.
• RAREFACTION: the most stretched part in a waveform
• AMPLITUDE (A): how much the particles are stretched or
compressed. The amount of energy carried by a wave is directly
related to the amplitude of the wave.
• WAVELENGTH (λ): the distance from one compression to the
next compression, or from one rarefaction to the next rarefaction.
• PERIOD (T): the time from one compression to the next
compression, or from one rarefaction to the next rarefaction.
• FREQUENCY (f): number of cycles per unit of time. (1/T)
Energy Transport and the
Amplitude of a Wave
• A wave is an energy transport phenomenon which transports energy
along a medium without transporting matter.
• The amount of energy carried by a wave is related to the amplitude
of the wave. A high energy wave is characterized by a high
amplitude; a low energy wave is characterized by a low amplitude.
• The amplitude of a wave refers to the maximum amount of
displacement of a particle on the medium from its rest position.
Frequency and speed
• The quantity frequency is not speed.
• The wave speed refers to HOW FAST the wave is
moving (m/s).
• The wave frequency refers to HOW OFTEN the
medium vibrates up and down. (# of cycles/second or
Hz).
• A wave can vibrate back and forth very frequently,
yet have a small speed; and a wave can vibrate back
and forth with a low frequency, yet have a high
speed. Frequency and speed are distinctly different
quantities.
Example #1
•
Find the amplitude and wavelength of
wave A, B, C.
Example #2
• A longitudinal wave moves to the right through a uniform
medium, as shown below. Points A, B, C, D, and E
represent the positions of particles of the medium.
1. Describe the motion of the particle at position C.
2. Which two points represent the wavelength of this
wave?
Example #3
•
1.
2.
3.
4.
The diagram represents waves A, B, C, and D
traveling in the same medium. Which two
waves have the same wavelength?
A and B
A and C
B and D
C and D
Example #4
•
In the diagram, the distance between
points A and B on a wave is 5.0
meters. What is the wavelength of this
wave?
2.0 m
phase
• Points on a periodic wave moving in the same direction
and having the same displacement from their rest
position (same up or same down) are said to have the
same phase, or to be “in phase.”
• Points on a periodic wave having the opposite
displacement from their rest position are said to have
be “out of phase”
Points A & E are in
phase
Points C & E are out of phase.
Points B & F are not
in phase b/c B is
going up, F is going
down
• If two points are in phase, they could only be multiple of
wavelength apart, such as 1λ (360o), 2λ (720o), 3λ(1080o), …
• If two points are out of phase, they could only be multiple of
half wavelength apart, but not whole wavelength apart, such
as ½ λ (180o), 1½ λ (540o), 2½ λ (900o),…
Points in phase:
A, C, & E
B, D
points are out of phase:
A, B
A, D
B, C
B, E
example
• Points in phase:
–
–
–
–
–
A&F
D&I
C&H
B&G
E&J
• Points out of phase:
–
–
–
–
B & E,
E & G,
G & J,
B&J
example
•
1.
2.
3.
4.
Which point on the wave diagram is in
phase with point A?
E
B
C
D
example
• The diagram shows a parked police car with a siren
on top. The siren is producing a sound with a
frequency of 680 hertz, which travels first through
point A and then through point B, as shown. The
speed of the sound is 340 meters per second.
• If the sound waves are in phase at points A and B, the
distance between the points could be
1. 1λ
2. ½ λ
3. 3∕2 λ
4. ¼ λ
Wave Velocity
Waves have a definite direction of travel.
• Wave period (T) = TIME FOR ONE WAVE CYCLE
• Wavelength (λ)= DISTANCE FOR ONE WAVE CYCLE
Equation
v

T
 f
Variables Affecting Wave Speed
•
The speed of a wave is not dependent upon properties
of the wave itself (frequency, period, amplitude,
wavelength). Rather, the speed of the wave is
dependent upon the properties of the MEDIUM
ONLY. Only an alteration in the properties of the
medium will cause a change in the speed.
Example #1
• What is the time required for the sound
waves (v = 340 m/s) to travel from the
tuning fork to point A?
Example #2
• A teacher attaches a slinky to the wall and
begins introducing pulses with different
amplitudes. Which of the two pulses (A or
B) below will travel from the hand to the
wall in the least amount of time?
3/26 do now
• The diagram below represents a circuit
consisting of two resistors connected to a
source of potential difference. What is the
current through the 20.-ohm resistor?
Homework – castle learning
Example #3
An automatic focus camera is able to focus on objects by
use of an ultrasonic sound wave. The camera sends out
sound waves that reflect off distant objects and return to
the camera. A sensor detects the time it takes for the
waves to return and then determines the distance an
object is from the camera. The camera lens then focuses
at that distance. Now that's a smart camera! If a sound
wave (speed = 340 m/s) returns to the camera 0.150
seconds after leaving the camera, then how far away is
the object?
summary
• Wave speed is dependent upon medium
properties
• Even though the wave speed is calculated by
multiplying wavelength by frequency, an
alteration in wavelength DOES NOT affect wave
speed.
• Rather, an alteration in wavelength affects the
frequency in an inverse manner. A doubling of
the wavelength results in a halving of the
frequency; yet the wave speed is not changed.
Wave speed of light and sound
• The speed of light is 3.00 x 108 m/s in air
or vacuum.
• The speed of sound at STP is 3.31 x 103
m/s.
Examples
1. What is the time required for light to travel
a distance of 1.5 × 1011 meters?
2. Sound waves with a constant frequency
of 250 hertz are traveling through air at
STP. What is the wavelength of the
sound waves?
Class work
• Worksheet 5.1.3 packet – due
today/tomorrow
Lab – period of a pendulum
Purpose :To determine
How amplitude affect period?
How length affect period?
How mass affect period?
Material :computer string Vernier computer interface 2 ring stands and pendulum
clamp, Logger Pro, Vernier Photogate, meter stick, protractor
Data section (20 pt):
–
The Data Section should include two tables of data with labeled column
headings (and units) to demonstrate a systematic study of the effect of
amplitude and length upon the period of the pendulum.
Data analysis (20 pt):
–
One graph shows the relationship between amplitude(x) and period (y)
–
One graph shows the relationship between length(x) and period (y).
–
One graph shows the relationship between mass (x) and period (y).
Conclusion (10):
–
The Conclusion section should respond to the three questions raised in
the Purpose.
PROCEDURE
1. Use the ring stand to hang a mass from a string.
2. Attach the Photogate to the second ring stand. Position it so that the mass blocks the
Photogate while hanging straight down. Connect the Photogate to DIG/SONIC 1 on
the interface.
3. Open the file “14 Pendulum Periods” in the Physics with Computers folder. A graph
of period vs. time is displayed.
4. Temporarily move the mass out of the center of the Photogate. Notice the reading in
the status bar of Logger Pro at the bottom of the screen, which shows when the
Photogate is blocked. Block the Photogate with your hand; note that the Photogate is
shown as blocked. Remove your hand, and the display should change to
unblocked. Click and move your hand through the Photogate repeatedly. After the
first blocking, Logger Pro reports the time interval between every other block as the
period. Verify that this is so.
5. Now you can perform a trial measurement of the period of your pendulum. Pull the
mass to the side about 10º from vertical and release. Click
and measure the
period for five complete swings. Click . Click the Statistics button, , to calculate the
average period. You will use this technique to measure the period under a variety of
conditions.
6. To determine how the period depends on amplitude, measure the period for five
different amplitudes using the protractor so that the mass with the string is released
at a known angle. Repeat Step 5 for each different amplitude. Record the data in
your data table.
7. To determine how the period depends on length, measure the pendulum length from
the rod to the middle of the mass and use the data for amplitude of 20º. Exchange
data with other groups. Record the data from each group of same amplitude, same
mass, different length in the second data table.
DATA TABLES
Amplitude (200g)
Amplitude (°)
Average Period (s)
Length (200 g, 10o)
Length
Average period
5
(cm)
(s)
9
12
100
90
70
60
50
15
Mass (10o)
Mass (g)
50
100
200
Average period (s)