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?
Transcript
3/23 do now – on a new sheet1. 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?
Lesson 1: Vibrations
Lesson 2: The Nature of a Wave
Lesson 3: Properties of a Wave
Introduction to Waves - Chapter Outline
Homework: castle learningPeriod 8 – electricity unit exam part I is on castle learning
Vibrational MotionA 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.
• 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.
• Objects that have a relatively short period (i.e., a low value for period) are said to have a high frequency.
1T
f
Check Your Understanding1. A pendulum is observed to complete 23 full cycles in 58
seconds. Determine the period and the frequency of the pendulum.
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?
Pendulum Motion is Periodic• 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.
FTen
Fgrav
Fnet
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.b. restoring force is the greatest.c. speed is the greatest.d. potential energy is the greatest e. kinetic energy is the greatest.f. total mechanical energy is the greatest.
sameA
A,C
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.
• 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.
• Where l is the length of the string in meters, T is the period in seconds, g = 9.81 m/s2
The period of pendulum
g
lT 2
graphs
Length (m)
perio
d
Period vs. length
perio
d√Length (m)
Period vs. √length
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:
T = 12 s
g = 9.81 m/s2
Unknown:
l = ?
Solve:
T = 2π√l/g
l = 36 m
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
b. Calculate the frequency of the pendulum.
c. Use the period of the pendulum to calculate the length of the pendulum string.
3/24 do now• A piece of coper wire with a cross-
sectional 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.
B.Resistivity will decrease.
C.Resistivity will not change.
Explain your answer
homework: castle learningPd. 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• The diagram shows an antenna emitting an
electromagnetic wave. In what way did the electrons in the antenna produce the electromagnetic wave?
1. by remaining stationary
2. by moving at a constant speed upward, only
3. by moving at a constant speed downward, only
4. by accelerating alternately upward and downward
• How are electromagnetic waves that are produced by oscillating charges and sound waves that are produced by oscillating tuning forks similar?
1. Both have the same frequency as their respective sources.
2. Both require a matter medium for propagation. 3. Both are longitudinal waves. 4. Both are transverse waves.
example
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
• The size of crest or trough determines the amount of energy in a wave
crest
trough
.
example
• A characteristic common to sound waves and light waves is that they
1. are longitudinal
2. are transverse
3. transfer energy
4. travel in a vacuum
Check Your Understanding1. 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
• 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?
a. down, only
b. up, only
c. down, then up
d. up, then down
• 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. A b. B c. C d. D
Example #2
• 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.
vExample #3
• 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?
Example #4
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 Wave – particles of the medium move PERPENDICULAR to the wave’s direction of travel
TRANSVERSE waves vs. LONGITUDINAL waves
Longitudinal Wave – particles of the medium move PARALLEL to the wave’s direction of travel.
Examples of Longitudinal and transverse wave
• Transverse: – Wave on a string– Stadium wave– Wave on a slinky– ELECTROMAGNETIC WAVES (light, RADIO,
microwaves, UV rays, etc)
• Longitudinal: – SOUND WAVE– Wave on slinky– Earthquake
• 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
3. the same
4. four times as great
Explain your answer
Example • 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
1. transverse wave of constant amplitude
2. longitudinal wave of constant frequency
3. mechanical wave of varying frequency
4. electromagnetic wave of varying wavelengths
Example • An electric bell connected to a battery is sealed inside a
large jar. What happens as the air is removed from the jar?
1. The electric circuit stops working because electromagnetic radiation cannot travel through a vacuum.
2. The bell's pitch decreases because the frequency of the sound waves is lower in a vacuum than in air.
3. The bell's loudness increases because of decreased air resistance.
4. The bell's loudness decreases because sound waves cannot travel through a vacuum.
Example • Which pair of terms best describes light waves
traveling from the Sun to Earth?
1. electromagnetic and transverse
2. electromagnetic and longitudinal
3. mechanical and transverse
4. 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
Transverse Wave – particles of the medium move PERPENDICULAR to the wave’s direction of travel
Motion of particles in the medium
v crest
trough
wavelength (λ)
A
amplitude
The Anatomy of a transverse wave
TRANSVERSE WAVECrest, 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)
Longitudinal Wave – particles of the medium move PARALLEL to the wave’s direction of travel.
rarefaction
compression
Motion of particles in the
medium
v wavelength (λ)
SOUND WAVESFaster in DENSE mediums
The Anatomy of a longitudinal wave
LONGITUDINAL WAVECompression, 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.
• Find the amplitude and wavelength of wave A, B, C.
Example #1
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
• The diagram represents waves A, B, C, and D traveling in the same medium. Which two waves have the same wavelength?
1. A and B
2. A and C
3. B and D
4. 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 C & E are out of phase.
Points B & F are not in phase b/c B is going up, F is going down
Points A & E are in phase
• 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
• Which point on the wave diagram is in phase with point A?
1. E
2. B
3. C
4. 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 VelocityWaves have a definite direction of travel.
• Wave period (T) = TIME FOR ONE WAVE CYCLE
• Wavelength (λ)= DISTANCE FOR ONE WAVE CYCLE
Equation
f
Tv
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
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?
Example #3
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.
Examples1. 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 pendulumPurpose :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.
PROCEDURE1. 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.
