WarmUp February 1718 2016 Vibrations and Waves Chapter 14 A periodic motion repeats in a regular cycle Examples include Pendulums such as on a grandfather clock A mass at the end of a spring ID: 797612
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Slide1
Where do we encounter waves? Write down all the examples of waves that you can think of.
Warm-Up: February 17/18, 2016
Slide2Vibrations and Waves
Chapter 14
Slide3A periodic motion repeats in a regular cycle.
Examples include:
Pendulums (such as on a grandfather clock)
A mass at the end of a spring
Vibrating guitar stringThe period is the amount of time for one complete cycle.The amplitude is the maximum amount that the object moves from its equilibrium position
Periodic Motion
Slide4Periodic Motion Graph
x
Slide5When you stretch or compress a spring, the spring exerts a force to return it to its equilibrium position.
The amount of force is given by
Hooke’s Law
where
is the spring constant (a property of the individual spring)and
is the distance the spring is displaced from its equilibrium position
Springs
Slide6How much force is needed to stretch a spring 25 cm if the spring constant is 105 N/m?
Example 1
Slide7How much force is needed to compress a spring 12 cm if the spring constant is 84 N/m?
You-Try #1
Slide8Stretching or compressing a spring also generates elastic potential energy
Energy of Springs
Slide9A spring has a spring constant of 256 N/m. How far must it be stretched to give it an elastic potential energy of 48 J?
Example 2
Slide10How far must a spring with a spring constant of 444 N/m be compressed to produce an elastic potential energy of 8.25 J?
You-Try #2
Slide11Read Chapter 14Page 378 #1-5
Assignment
Slide12Slide13You will be assigned to a group.
Your group’s goal is to experimentally show how each of the following affect
the period of an oscillation (the time it takes to complete one cycle).
The mass at the end of the string
The length of the stringThe angle of oscillation (keep
from vertical)
Materials allowed:
String (and scissors to cut the string)
Masses
Rulers/
Metersticks
/ProtractorsStopwatch (cell phone)
TapeBe sure to record everything (procedures and data)
Today’s Lab – Feb. 19, 2016
Slide14Leader:
Keep group on task
Collect and return supplies
Determine who performs each part of the lab (timing, etc.)
Procedures recorder:Write down everything that your group does (whether it ends up working or not)Data recorder:Write down all dataHelper (2nd period only):
Fill in for any absent group member(s)
Assist group members as needed.
Lab Roles
Slide15Leader
Procedures Recorder
Data Recorder
Group 1
Le, Dylan
Luu, Justin
Suri, Anirudh
Group 2
Kim, Younghoon
Harris, Samantha
Remigio, Allexa
Group 3
Wong, Gracie
Manam, Abhinav
Bantigue, Alanna
Group 4
Yue, Linton
Sitapati, Kedar
Roos, Spencer
Group 5
Nguyen, Austin
Bey, Jack
Swartz, Erika
Group 6
Herring, Grace
Ton, Tyler
Townsend, Jaren
Group 7
Kim, Sean
Clarke, Jacob
Wadhwa, Sahil
Group 8
Marasigan, Emmanuel
Howo, Michael
Jewell, Katherine
Group 9
Hill, MeganJulazadeh, HanaHill, Megan
Lab Groups – Period 3
Slide16Leader
Procedures Recorder
Data Recorder
Helper
Group 1
Bhushan
,
Somil
Sandfer, Connor
Gupta, Mihir
Kye, Johanna
Group 2
Kapoor, Pia
Laudenslager, Alexis
Wedge, Lauren
Pennington, Julia
Group 3
Lodge, Grace
Lee, Rudolph
Hagstrom, Erik
Folkl, Julia
Group 4
Nguyen, Haley
Rao,
Ananya
Obermiller, Andrew
Nguyen, Wendy
Group 5
Thomas, Zoe
Almond, Amber
Hardisty, Sabrina
Sharma, Amitesh
Group 6
Nagelvoort, Christopher
Andersen, Blake
Calkins, Nicholas
Castaneda, Ernesto
Group 7
Yang, JerryKwan, CrystalImler, CarsonPadmanaban, SnehaGroup 8Jones, CameronWaldman, PhilipBrana, Jennifer
Lab Groups – Period 2
Slide17Slide18A spring is compressed by a 22 N force, giving it a potential energy of 2.016
J.
What is the spring constant of the spring?
How far was the spring compressed?
Warm-Up: February 22, 2016
Slide19How does mass/length/angle affect the period?
No effect?
Linear effect? If so, what is the equation of the line?
Non-linear effect? If so, what function is it (exponential, logarithmic, quadratic, etc.)?
Combine your results to write an equation for the period in terms of mass, length, and angle.The equation may also include constants.Compare your experimental result with the textbook equation. Why are they different?
Lab Conclusions
Slide20Must be typed
One copy per lab group
Graphs must be computer generated (such as with Excel, Google Docs, etc.)
Procedures recorder should type procedures
Data recorder should type raw dataGroup should work together on:IntroductionGraphs and data analysisConclusionsLab Report
Slide21You will be assigned to a group.
Your group’s goal is to experimentally show how each of the following affect
the period of an oscillation (the time it takes to complete one cycle).
The mass at the end of the string
The length of the stringThe angle of oscillation (keep
from vertical)
Materials allowed:
String (and scissors to cut the string)
Masses
Rulers/
Metersticks
/ProtractorsStopwatch (cell phone)
TapeBe sure to record everything (procedures and data)
Finish the Lab
Slide22Slide23A small marble
is pressed down on a vertical spring
, causing the spring to compress 3.0 cm from its equilibrium position. The marble is released, and the spring shoots it straight up into the air. How high above the spring’s equilibrium position does the marble reach?
Warm-Up: February 23, 2016
Slide24Small-diameter mass, called the pendulum bob
String has negligible mass, but strong enough to not stretch appreciably
Undergoes simple harmonic motion if
The Simple Pendulum
Slide25Simple Pendulum
Slide26Period of Simple Pendulum
Period
is the amount of time for one cycle.
Represented by a capital
.
Measured in seconds, s.
Slide27Frequency
is the reciprocal of period.
Represented by lower case
.
Measured in Hertz, Hz1 Hz = 1/s
Frequency
Slide28Does not depend on mass.
Does not depend on amplitude (for
)
Can be finely adjusted, and can make excellent clocks.
Can also be used to solve for
.
Period of Simple Pendulum
Slide29What is the acceleration due to gravity in a region where a simple pendulum having a length of 75.000 cm has a period of 1.7357 s?
You-Try #3
Slide30What is the effect on the period of a simple
pendulum if you double its length?
Think-Pair-Share
Slide31What is the length of a pendulum that has a period of 0.500 s? Let g=9.80 m/s2
.
You-Try #4
Slide32The pendulum on a cuckoo clock is 5.00 cm long. What is its frequency? Let g=9.80 m/s
2
.
You-Try #5
Slide33Resonance occurs when small forces are applied at regular intervals to an object in periodic motion causing the amplitude to increase.
Resonance
Slide34Write down as many examples of resonance that you can think of.
Think-Pair-Share
Slide35Examples include:Pushing someone on a swing
Jumping on a diving board
Wind on the
Tacoma Narrows Bridge
Resonance
Slide36Read Section 14.1Page 379 #6-8
Page 380 #9-13
Read Section 14.2
Assignment
Slide37Slide38A spring has a spring constant of 125 N/m. It is attached to the ceiling and a block is attached to the bottom. The spring is stretched 20.0 cm.
Draw a free body diagram of the block.
What force does the spring exert on the mass?
What is the weight of the block?
What is the elastic potential energy stored in the spring?
Warm-Up: February 24/25, 2016
Slide39Homework Questions?
Slide40A wave is a disturbance that
carries energy
through matter or space
A wave usually does NOT transfer mass, only energy
A wave pulse is a single bump or disturbance. Most waves are a series of wave pulses.Two main types of waves:Mechanical waves – travel through matterElectromagnetic waves – do not require matter, can travel through a vacuum
Waves
Slide41Examples include:
Water waves
Sound waves
Waves on a rope
Waves on a springMechanical waves require a medium (matter) through which they propagate (travel).Three main categories:Transverse WavesLongitudinal WavesSurface Waves
Mechanical Waves
Slide42A transverse wave is one that vibrates perpendicular to the direction of the wave’s motion
A wave on a rope is an example of a transverse wave
Simulation
Transverse Waves
Slide43Crest – The highest point
Trough
– The lowest point
Amplitude
– The maximum displacement of of the waveThe higher the amplitude, the greater the amount of energy transferred.Wavelength – The distance between crests (or the distance between troughs)Parts of a Transverse Wave
Slide44Identify which point(s) correspond with each of the following: crest, trough, amplitude, wavelength
Think, Pair, Share
Slide45Slide46Slide47A
longitudinal wave
is one whose disturbances are in the same direction as (parallel to) the direction of the wave’s motion
Sound waves are longitudinal
Waves from a compressed spring are longitudinal
Longitudinal Waves
Slide48Compression – A dense part of a longitudinal wave
Rarefaction
– A low density part of a longitudinal wave
Wavelength
– The distance between compressions (or the distance between rarefactions)Parts of a Longitudinal Wave
Slide49Slide50Slide51A man with a mass of 75 kg hangs from a spring that is attached to the ceiling, causing it to stretch 83 cm (after the oscillations stop). What is the spring constant of the spring?
Warm-Up:
Slide52Surface waves are waves with characteristics of both transverse and longitudinal waves.
Ocean waves are a prime example of surface waves.
The paths of individual particles are circular.
Surface Waves
Slide53The following are all used to measure and/or describe waves:
Wave Speed
Amplitude
Period
FrequencyWavelengthMeasuring Waves
Slide54Wave Speed
– The distance a wave travels per unit time
Represented by a lower case
Measured in meters per second, m/s
Depends on the medium through which the wave is travelling
Wave Speed
Slide55Amplitude – The maximum displacement of a wave from its at-rest position
Represented by a capital
Measured in meters, m
Depends on how the wave was generated
Does not depend on the wave speed or the mediumMore work must be done to generate larger amplitude waves.
Waves with larger amplitudes transfer more energy
Amplitude
Slide56Period
- the amount of time for one complete cycle/oscillation
Represented by a capital
Measured in seconds
Depends only on the wave sourceDoes not depend on the wave speedDoes not
depend on the medium
Period
Slide57Frequency – The amount of cycles/oscillations per second
Represented by a lower case f
Measured in Hertz, Hz
Depends only on the wave source
Does not depend on the wave speedDoes not depend on the mediumFrequency
Slide58Wavelength
– Length of a cycle (distance between similar points)
Distance between crests (or troughs) of a transverse wave
Distance between compressions (or rarefactions) of a longitudinal wave
Represented by Greek letter lambda, Measured in meters
Wavelength
Slide59Sound waves travel approximately 340 m/s in air. What is the wavelength of a sound wave that has a frequency of 170 Hz?
You-Try #5
2.0 m
Slide60Sound has a speed of 3100 m/s in copper. What is the wavelength of the wave from Example 3 after it crosses into a copper medium?
You-Try #6
18 m
Slide61Read Section 14.2Page 386 #15-25
Read Section 14.3
Assignment
Slide62Slide63Slide64A sound wave produced by a clock chime is heard 515 m away 1.50 s later.
What is the speed of the clock’s chime in air?
If the sound wave has a frequency of 436 Hz, what is the period of the wave?
What is the wave’s wavelength?
Warm-Up:
Slide65Homework Questions?
Slide66What happens when a wave reaches the end of its medium?When the
incident wave
reaches the end of its medium,
some or all of the energy is reflected back as a reflected wave.Some reflected waves are inverted, such as waves on a rope with a fixed end (as in the simulation)Wave Reflection
Slide67The principle of superposition
states that the amplitude of passing wave pulses is additive.
If pulses are on opposite sides, one amplitude is negative (adding a negative
subtracting)
The result of superposition is called interference.
Superposition
Slide68Superposition Examples
Slide69Interference can cause
standing waves
, which appear to not propagate.
Example: Rope moves up and down, but no wave pulses move to either side.
The nodes are points that do not move.The antinodes are the points that move the most.Simulation: Amplitude=20, Frequency=30, Damping=0, Tension=high-1
Standing Waves
Slide70Slide71Stringed instruments depend on standing waves to make music.
These standing waves are called
harmonics
.
Standing Waves in Music
Slide72A wave has a frequency of 225 Hz. What is its period?The wave changes medium from air to water. What happens to the period?
(increase, remain constant, or decrease)
Warm-Up:
Slide73Homework Questions?
Slide74Often represented by a wave front
, a line that represents a wave crest.
Waves move perpendicular to the wave front, often represented by a
ray
.Waves in Two Dimensions
Slide75The
law of reflection
states that the angle of incidence equals the angle of reflection
Reflection of 2-D Waves
Slide76Read Chapter 14Page 396 #31, 32, 33, 41, 42, 52, 56, 69, 71, 72, 76, 79, 81
Assignment