Unit 10: Waves and Sound
Lesson 1 - Vibrations and Waves
Read Chapter 25 “Vibrations and waves” in Conceptual Physics
1.1 Web Walk – Waves and Wave Properties
Concept Development 25-1
Collaborate Reflection:
1.2 Lab Activity – Tick-Tock Hickory Dickory Dock
1.3 Problem Solving Activity – Waves and Vibrations
1.4 Lab Activity – Doppler Effect
Knowledge Check
1.5 Quiz – Waves and Vibrations
Read Chapter 26
Lesson 2 - Sound
2.1 Quick Lab – Pitch and Medium
2.2 Web Walk – Sound Waves
Concept Development 26-1
2.3 Lab Activity – Determining the Speed of Sound
Physics in Action
2.4 Quick Lab – The Tacoma Narrows Bridge Collapse
Collaborative Reflection
2.5 Quiz – Sound
Lesson 3 – Unit Test
Learning Goals
By the end of this unit, you will be able to:
* describe the characteristics and properties associated with waves
* recognize the relationship between period and frequency
* recognize the relationship between pitch and frequency
* recognize the relationship between energy and amplitude
* distinguish between a transverse wave and a longitudinal wave
* distinguish between constructive and destructive interference
* identify the conditions associated with simple harmonic motion
* give examples of common applications involving waves
* calculate the period and/or the frequency of an object in simple
harmonic motion
* apply the universal wave equation (v = λ f) to solve problems involving:
wave speed
frequency
wavelength
* describe and give examples of the following wave phenomena and the
conditions that produce them:
resonance
beats
forced vibrations
interference (superposition principle)
constructive and destructive interference
Doppler shift
standing waves
* describe factors that affect the speed of sound
* calculate the speed of sound when given the frequency and the
temperature
Wave motion is described as the transfer of energy without the transfer of
mass. Energy is transferred to bowling pins by rolling a bowling ball at
them. This is not wave motion since the energy was accompanied by the
mass of the bowling ball, this is mass transfer. If one could shout loud
enough, we could knock over the bowling pins by yelling at them. In this
case, no mass is transferred to the bowling pins. The energy is transferred
through the air by collisions between air molecules to the bowling pins.
This interaction between molecules must occur so that the wave can be
passed on to the next. Most of the information around us gets to us in
some form of wave.
The simplest form of wave motion can be demonstrated by creating a
single disturbance (pulse) in a medium. The sounds we hear are carried by
a mechanical disturbance through a medium such as air. Sound also
travels through liquids and solids. The source of sound is a vibrating object
such as – a guitar string, air column, speaker cone, piano sounding board,
and a saxophone reed.
By the end of this unit, you will be able to answer this question: What do
pendulums, slinkys, metronomes, grandfather clocks, suspension bridges,
trapeze acrobats, wind instruments, bells, orchestras, pitch pipes, surfing,
and shock absorbers have in common?
Lesson 1: Vibrations and Waves
Simple harmonic motion! While sitting in church at a Cathedral in Pisa ,
Galileo was watching a swinging chandelier. The chandelier was set in
motion after it was bumped while a person was lighting the candles.
Galileo is said to have measured the frequency by timing the swings with
his pulse. Galileo is credited as the first person to notice that the motion of
a pendulum depends on its length and is independent of the mass and the
amplitude.
Remember when – As a child learning to “pump” on a play ground swing;
playing with a slinky on the floor or the stairs; winding the jack-in-the-box
until jack pops up; swinging on the monkey bars; and jumping on the bed!
As you begin your study of SHM (simple harmonic motion), you will be able
to explain your childhood physics adventures! By the end of the lesson,
you will be able to explain – What do pendulums, slinkys, metronomes,
grandfather clocks, suspension bridges, trapeze acrobats, and shock
absorbers have in common?
10.1.1 Waves Web Walk
It is important to go to the sites in order and follow the directions as
given. If there is a related assignment, it will be clearly indicated. You may
want to take notes as you move along the Web Walk.
Go to www.physicsclassroom.com/Class/waves/wavestoc.html The
Physics Classroom (Physics Tutorial)
Click on Lesson 1 “The Nature of a Wave” and complete Waves and
Wavelike Motion . Note the diagrams.
Click NEXT to go to What Is A Wave? and complete the lesson. Note
the bold red terms as well as the blue links, view the animation, and do the
“Check Your Understanding”.
Click NEXT to go to Categories of Waves and complete the lesson. Note
the bold red terms as well as the blue links, view the animations, and do
the “Check Your Understanding”.
Click Go to Lesson 2 “Properties of Waves” and complete The Anatomy
of a Wave. Note the bold red terms as well as the blue links and do the
“Check Your Understanding”.
Click NEXT to go to Frequency and Period of a Wave and complete the
lesson. Note the bold red terms as well as the blue links and do the “Check
Your Understanding”.
Click NEXT to go to Energy Transport and the Amplitude of a Wave and
complete the lesson. Note the bold red terms as well as the blue links and
do the “Check Your Understanding”.
Click NEXT to go to The Speed of a Wave and complete the lesson.
Note the bold red terms and do the “Check Your Understanding”.
Click NEXT to go to The Wave Equation and complete the lesson. Note
the bold red terms and do the “Check Your Understanding”.
Click Go to Lesson 3 “Behavior of Waves” and complete Boundary
Behavior. View the animations for fixed end reflection. View the animation
for free end reflection. How are the reflections different?
View the animation that depicts the boundary behavior of a pulse which
is moving along a less dense medium towards a more dense medium.
What happens when the pulse reaches the end of the less dense
medium? Do the “Check Your Understanding”.
Go to physicsclassroom.com/Class/waves/U10L3c.html The Physics
Classroom (Physics Tutorial) and complete the Interference of Waves .
Note the bold red terms and do the “Check Your Understanding”.
How is constructive interference different from destructive
interference? What is the principle of superposition?
Click NEXT to go to The Doppler Effect and complete the lesson. What
is the red shift? What is the blue shift?
Click Go to Lesson 4 “Standing Waves” and complete Traveling Waves
vs, Standing Waves. View the animation for a standing wave pattern.
Click NEXT to go to Formation of Standing Waves and complete the
lesson. Note the bold red terms. What is a standing wave?
Click NEXT to go to Nodes and Antinodes and complete the lesson.
Note the bold red terms and the animation. Do the “Check Your
Understanding.”
Analysis:
Consider the following questions and record your responses to
your notebook:
1. Calculate the wavelength of your favorite radio station.
2. With respect to the direction of the wave's motion, how do the directions
of vibrations differ for transverse and longitudinal waves?
3. What is a standing wave?
4. How is constructive interference different from destructive interference?
5. What is the principle of superposition?
6. Can waves overlap in such a way to produce a zero amplitude?
7. The waves are more crowded in front of a swimming bug and more
spread out behind. Is the wave speed greater in front of the bug and less
behind the bug?
8. What is the red shift? What is the blue shift?
9. Does the Doppler effect occur only for some types of waves or all types
of waves? Explain.
Collaborate Reflection:
Go to the Threaded Discussion and respond to this reflection defending
your position. Respond to at least two other persons with a thoughtful
comment – more than “I agree” or “You are right”.
Imagine you are sitting in small boat on a calm lake. A stone thrown in
the water makes a splashing noise and some ripples. Predict whether the
boat will oscillate before, after, or at the same time that you hear the
splash. Justify your prediction.
10.1.2 Lab Activity – Tick -Tock Hickory Dickory Dock
A swinging pendulum keeps a very regular beat. It is so regular that for
many years the pendulum was the “heart” of clocks used in astronomical
measurements at the Greenwich Observatory. A simple pendulum consists
of a small heavy ball (bob) suspended by a lightweight string from a rigid
support. The bob is free to swing back and forth, oscillate, in any direction.
The time it takes to complete one back and forth cycle is called its period.
Problem: What characteristics of a pendulum determine its period?
Procedure:
1. Using a weight (bob), set up a pendulum with a length of 70. cm.
Measure its period three times and record the data in the data table.data
sheet
2. Shorten the pendulum length by 5. cm. Measure its period three
times and record the data in the data table.
3. Complete the data table for the remaining pendulum lengths.
4. Plot a graph of the period (vertical axis) versus the length of the
pendulum (horizontal axis). Is the graph a straight line showing that the
period is directly related to the length? ______
Is it a curve showing that the relationship between period and length
is not a direct relationship? ______
5. Often the data points are on a curve that is not a straight line. It is
difficult to determine the relationship between two variables from such a
curve. Experimenters try to produce a straight line graph by plotting
functions (squares, cubes, etc.) of the variables that were originally used
on the vertical and horizontal axes. A straight line graph is easier to use to
determine the relationship between variables. The simplest way to
“straighten out” a curve is to see if one of the variables is proportional to a
power of the other variable. If your graph of period vs. length curves
upward, perhaps period is proportional to the square or the cube of the
length. If your graph of period vs. length curves downward, perhaps the
square or cube of the period is proportional to the length. Plot some
powers of one variable against the other to see if you can produce a
straight line graph from your data.
What powers of length and/or period results in a straight line graph?
_____________________
Analysis:
Reflect on the following questions relating to the pendulum
activity.
1. From your graph, predict the length of a pendulum that has a period of
2.0 s.
2. What effect, if any, does length have on the period of a pendulum?
3. What principle from mechanics accounts for the different periods of
pendulums of different lengths?
4. Why is a pendulum a reliable time-keeping device, even if its oscillations
gradually decrease in amplitude over time?
5. If you set up your pendulum aboard the orbiting space station, would the
period be less than, the same as, or greater than it would be in your lab?
6. If you set up your pendulum atop Mt. Everest , would the period be less
than, the same as, or greater than it would be in your lab?
7. From your graph of T2 vs. L determine the value of “g.”
10.1.3 Problem Solving Activity – Waves & Vibrations
Using the equations (relationships) from the Conceptual Physics
textbook and the Formula/Information Sheet for ILO Physics , complete the
following situations. Remember to list the information (analyze), plan the
solution (formula used), solve the relationship (substitute in values), and
check the answer for proper units. PSYW (Please Show Your Work).
A. Go to the Plug and Chug on page 388 in your text and solve
problems 22 and 25.
B. Go to the Think and Solve on page 389 in your text and solve
problem 36.
C. Go to the Practice Problems on page 681 in your text and solve
problems 3 and 5.
D. Gary Stewart of Reading , OH set a pogo stick record in 1990 by
jumping 177,737 times. If the pogo stick he used had a force constant of
6000. N/m and was compressed 0.12 m on each jump, what force must
Gary have exerted on the pogo stick upon each jump? (Hint: Hooke's Law)
E. A spider swings in the breeze from a silk thread with a period of 0.6 s.
How long is the spider's silk thread?
Submit your completed assignment to your notebook.
10.1.4 Lab Demonstration – The Doppler Effect
Go to www.kettering.edu/~drussell/Demos/doppler/doppler.html (
Kettering University ) “Doppler Effect and Sonic Booms”.
1. Click on the car horn to observe the Doppler shift.
2. Look at the Stationary Sound Source movie. Notice how the sound
waves originate from the source.
3. Look at the Sound Source Moving at Mach 0.7. This is less than the
speed of sound. Notice difference in the frequency and wavelength of the
waves behind and in front of the sound source.
4. Look at the Sound Source Moving at Mach 1.0 (Breaking the Sound
Barrier). Notice the pressure front (barrier) that must be broken to reach
supersonic speeds.
5. Look at the Sound Source Moving at Mach 1.4 (Supersonic speed).
Notice the formation of the “Mach cone” which forms a “shock wave” or a
“sonic boom.”
6. Check out the applications of the Doppler Effect.
Go to lectureonline.cl.msu.edu/~mmp/applist/doppler/d.htm (Lecture
Online MSU) “Doppler Effect.”
1. Set the Mach speed at 0 and observe the wave pattern.
2. Set the Mach speed at 0.5 and observe the wave pattern.
3. Set the Mach speed at 1.0 and observe the wave pattern.
4. Set the Mach speed at 1.5 and observe the wave pattern.
5. Set the Mach speed at 2.0 and observe the wave pattern.
Go to library.thinkquest.org/19537/java/Doppler.html (Oracle: Think
Quest) “Doppler Effect Applet” Interactively experience the Doppler Effect
by changing the speed of the plane. Notice the wave shift behind and in
front of the plane. Notice the waves reaching the observer.
Analysis: Consider the following questions and submit your
response to your notebook.
1. When a source moves toward you or away from you, is there an
increase or a decrease in the wave speed?
2. Describe the Doppler effect for sound and relate it to the red and blue
shifts for light.
3. Describe the wave pattern formed when the source moves at the same
speed as the waves.
4. What are bow waves and when do they form?
5. What is a shock wave and when do they form?
6. What is a sonic boom? a “water boom?”
Knowledge Check
Now that you have studied waves it is time to apply the knowledge you
have acquired from the activities in this lesson. You have been
commissioned by NASA to travel to Jupiter's innermost moon, Io, to learn
more about this volcanic satellite. As you board the spacecraft, you receive
your equipment and a set of directions for your mission. Your equipment
consists of a rock tied to a 10.0 cm string and a stopwatch and you are
asked to derive an experiment that would allow you to determine the
acceleration due to gravity on Io. You must use both pieces of equipment
and nothing more. 1) Describe how you would calculate Io's gravitational
acceleration. 2) If the pendulum swings with a period of 1.48 s, what is the
gravitational acceleration on Io?
10.1.5 Lesson Wrap Up – Quiz – Vibrations & Waves
Lesson 2: Sound
Have you ever been in a boat in the middle of a lake and been able to hear
sounds from the shore? When you make the sound of a race car going
around the track you very likely made a roaring sound that decreased in
pitch. Why? Why does the pitch of falling water at a water falls vary? In the
movies, the Native Americans would place their ears to the ground to listen
for approaching horses. Why? Sound is a mechanical disturbance moving
through a medium in a longitudinal (compression) wave. Sound can be
beneficial and pleasing or it can be distracting, and even cause damage to
buildings and the human body. Guitars, saxophones, pianos, pop bottles,
shopping malls, bridges, crystal glasses, trombones, and pipe organs have
a commonality – resonance! This lesson will help you understand the role
sound plays in our lives.
Activity 10.2.1 Quick Lab – Pitch and Medium
Problem: What is the relationship between the pitch of a sound and the
medium through which it travels?
Procedure:
1. Fill each of the five or six pop bottles with a different amount of water.
2. Tap on the side of each bottle with a wooden dowel (small piece of
wood). Note which bottle has the highest pitch and which one has the
lowest pitch.
3. Blow across the top of each bottle. Note which bottle has the highest
pitch and which one has the lowest pitch.
4. Adjust the water levels in the bottles so you can tap out or blow across
the bottle tops to play a simple tune for your classmates and instructor.
Analysis:
1. What vibrates when the bottles are tapped?
2. How did the amount of water affect the pitch?
3. How did the pitch vary when you blew across the top of the bottle?
4. What vibrates when you blew across the tops of the bottles?
5. As the length of the air column gets longer, what happens to the
frequency?
6. Does the pitch become higher as the frequency increases or the as
wavelength increases?
7. If salt water was used, what would happen to the frequency?
Submit your analysis to your notebook.
10.2.2 Sound Waves Web Walk
It is important to go to the sites in order and follow the directions as
given. If there is a related assignment, it will be clearly indicated. You may
want to take notes as you move along the Web Walk.
Go to www.physicsclassroom.com/Class/sound/soundtoc.html The
Physics Classroom – Sound Waves and Music (Physics Tutorial)
Click on Lesson 1 “The Nature of a Sound Wave” and complete Sound
is a Mechanical Wave . Check out the blue links, view the animation, and
do the “Check Your Understanding”.
Click NEXT to go to Sound is a Longitudinal Wave . Note the bold red
terms as well as the blue links and view the animation.
Click NEXT to go to Sound is a Pressure Wave. Note the bold red terms
as well as the blue links, view the animation, and do the “Check Your
Understanding”.
Click Go to Lesson 2 “Sound Properties and Their Perception” and
complete Pitch and Frequency. Note the bold red terms as well as the blue
links and do the “Check Your Understanding”.
Click NEXT to go to Frequency and Period of a Wave . Note the bold
red terms as well as the blue links and do the “Check Your
Understanding”.
Click NEXT to go to Intensity and the Decibel Scale and complete the
lesson. Note the bold red terms as well as the blue links and do the “Check
Your Understanding”.
Click NEXT to go to The Speed of Sound . Note the bold red terms as
well as the blue links and do the “Check Your Understanding”.
Go to www.physicsclassroom.com/Class/sound/U11L3a.html The
Physics Classroom - Behavior of Sound Waves (Physics Tutorial) and
complete the Interference and Beats . Note the bold red terms as well as
the blue links, view the animation, and do the “Check Your Understanding”.
Click NEXT to go to Doppler Effect and Shock Waves . Note the bold
red terms as well as the blue links and do the “Check Your
Understanding”.
Go to www.physicsclassroom.com/Class/sound/U11L4a.html The
Physics Classroom – Resonance and Standing Waves (Physics Tutorial).
Complete Natural Frequency noting the bold red terms as well as the blue
links and diagrams.
Click NEXT to go to Forced Vibration. Note the bold red terms as well as
the blue links.
Click NEXT to go to Standing Wave Patterns. Note the bold red terms
as well as the blue links and view the animations for the 1 st , 2 nd , and 3
rd harmonics.
Click NEXT to go to Fundamental Frequency and Harmonics. Note the
bold red terms as well as the blue links and do the “Check Your
Understanding”.
Click Go to Lesson 5 “Musical Instruments” and complete Resonance.
Note the bold red terms as well as the blue links and diagrams.
Click NEXT to go to Guitar Strings. Note the bold red terms, the blue
links, the practice problems, and do the “Check Your Understanding”.
Click NEXT to go to Open-End Air Columns. Note the bold red terms,
the blue links, the practice problems, and do the “Check Your
Understanding”.
Click NEXT to go to Closed-End Air Columns. Note the bold red terms,
the blue links, the practice problems, and do the “Check Your
Understanding”.
Questions to consider in your notebook:
1. What is the source of all sounds?
2. How dos pitch relate to frequency?
3. How does air temperature affect the speed of sound?
4. Why does sound travel faster in solids and liquids than gases?
5. What does it mean that everything has a natural frequency of vibration?
6. What is the relationship between forced vibration and resonance?
7. Is it possible for one sound wave to cancel another? Explain.
8. How does interference of sound relate to beats?
9. The sitar, an Indian musical instrument, has a set of strings that vibrate
and produce music, even though they are never plucked by the player.
These “sympathetic strings” are identical to the plucked strings and are
mounted below them. What is your explanation?
10. How much more intense is a close whisper than normal breathing?
Collaborate Reflection:
Respond to this reflection defending your position. Respond to at least
two other persons with a thoughtful comment – more than “I agree” or “You
are right”.
You may have noticed that there is a difference in the way ceilings,
walls, and furnishings are designed in different rooms such as auditoriums,
churches, libraries, concert halls, etc.. Why do the designers consider
many factors to accommodate the auditory function of the room?
10.2.3 Lab Activity – Mach One # 69 lab
Introduction:
Resonance, or sympathetic vibration, is the reinforcing of wave strength.
It occurs when the natural vibration rates of two objects are the same. The
air column in a closed glass tube produces its best resonance when it is
approximately one-fourth as long as the wavelength of the sound that it
reinforces. A small correction in wavelength must be made for the internal
diameter of the tube. The wavelength of the sound may be calculated from
the resonant length of the tube by using the equation λ = 4(L + 0.4d),
where λ (lambda) is the wavelength, L is the length of the resonant column
of the closed tube, and d is the diameter of the tube.
Analysis: Complete lab questions and the following questions in
your notebook
1. If a longer plastic tube were available, would it be possible to find
another position where resonance is produced? Explain.
2. How could you modify the experiment to find the resonant length of an
open pipe? Hint: For an open pipe wavelength is λ = 2(L + 0.8d).
3. Opera singers have been known to set crystal goblets in vibration with
their powerful voices. In fact, an amplified human voice can shatter the
goblet, but only at certain fundamental frequencies. Speculate about why
only certain fundamental frequencies will break glass.
4. An airplane mechanic (standing still) notices that the sound from a twinengine aircraft rapidly varies in loudness when both engines are running.
What could be causing this variation back and forth between loud and
soft?
5. The speed of sound is not always the same. Write a paragraph
explaining why this is so. Use the properties of temperature, density, and
phase of matter in your answer.
6. At 25 ºC, the speed of sound in air is 346 m/sec. At 0 ºC, the speed of
sound in air is 332 m/sec. Explain why the speed decreases as the
temperature decreases.
Physics In Action :
Inspiration Music Inc has commissioned you to develop a homemade
instrument display to demonstrate how physics concepts relate to the
design of musical instruments. Here are the guidelines for your instrument:
1. Each student must make one musical instrument. 2. The instrument is to
be made from common household materials. 3. The instrument must be
capable of producing a complete octave. 4. Each instrument must be
accompanied by a patent application that explains the workings of the
instrument and describes how physics principles apply to the instrument.
You are to use simple household items to design an instrument to present
and demonstrate to the class. Enjoy the challenge!
10.2.4 – Quick Lab – Tacoma Narrows Bridge Collapse
As the Tacoma Narrows Bridge ( situated on the Tacoma Narrows in
Puget Sound) near the city of Tacoma, Washington, was being built, it
would oscillate in the wind. After it was completed on July 1, 1940, it was
often closed to traffic on windy days. Shortly after the bridge was opened
to traffic it was christened “Galloping Gertie” by the people of the Tacoma
area. The residents in the area would come to watch the bridge oscillate
and many would make a sport of driving across the bridge on windy days.
On November 7, 1940, at approximately 11:00 AM, the first Tacoma
Narrows suspension bridge collapsed due to wind-induced vibrations. The
wind induced vibrations, caused the bridge to oscillate in a torsional mode
so greatly that it collapsed. A professor, who was on the bridge studying
the oscillations just before it collapsed, escaped to safety by running down
the center white line of the bridge.
In this lab we look at a particular mechanical system that ended up in
destructive oscillations. Your job will be to examine the information and try
to determine the cause of the bridge collapse.
Be mindful of the fact that this is not the only bridge to ever collapse.
Some have done so after years of neglect in their maintenance, others
were not structurally capable of withstanding the loads applied to them.
This one in particular, however, was newly built. It was designed to expand
and contract and move about to some degree.
Go to http://www.archive.org/details/SF121 watch video
Go to www.lib.washington.edu/specialcoll/exhibits/tnb/ (University of
Washington Libraries ) “History of the Tacoma Narrows Bridge ”.
1. Read the introduction noting the pictures in the document.
2. Click on Construction. As you look at the construction of the bridge, click
on “show image” to see the slide show of the construction.
3. Click on Opening and Experimentation and read through part 3 of the
history of the Tacoma Narrows Bridge.
4. Click on The Collapse . As you look at the collapse of the bridge, click
on “show image” to see the slide show of the collapse.
5. Click on Aftermath . As you look at the aftermath and the theories
about what would have saved this bridge, click on “show image” to see the
slide show of the aftermath.
Go to www.civeng.carleton.ca/Exhibits/Tacoma_Narrows/ “ Tacoma
Narrows Bridge ”. Click MPEG video clip to see the action showing the
maximum torsional motion shortly before failure.
Go to
www.civeng.carleton.ca/Exhibits/Tacoma_Narrows/DSmith/photos.html to
look at “A Case Study and Analysis of the Tacoma Narrows Bridge
Failure”. Clicking on the pictures will enlarge them for viewing.
Go to www.eng.uab.edu/cee/reu_nsf99/tacoma.htm#tnb
Questions to Consider:Place answers in your notebook
1. How did the wind influence the behavior of the bridge?
2. How could the wind cause the bridge oscillate in its resonant frequency?
3. What part of a standing wave is the center white line on the bridge?
4. How was the twisting motion established in the Tacoma Narrows
Bridge?
5. How can a steady horizontal wind cause the bridge to vibrate in a
vertical direction?
Reflection: Tomorrow's Technology!
Respond to this reflection defending your position. Respond to at least
two other persons with a thoughtful comment – more than “I agree” or “You
are right”.
Bridge inspectors visually search for cracks in the steel that can weaken
the bridge. David Prine, a research scientist at Northwestern University ,
thinks that the most reliable way to find damage is to listen to the bridge.
“When a piece of steel cracks, high-frequency sound is emitted,” states
Prine. These noises often sound like banging noises that echo through out
the bridge. What principles of physics are demonstrated by an acoustic
bridge inspection?
10.2.5 Lesson Wrap Up –Quiz – Sound