Download Chapter 9.2

Vote for the best TA
i-clicker-1
A. Samrat Dutta is very good
B. Samrat Dutta is ok/needs improvement
C. Ashley Carlton is very good
D. Ashley Carlton needs improvement
i-clicker-2
A. Maggie Baldwin is very good
B. Maggie Baldwin is ok/needs improvement
C. Calli Nguyen is very good
D. Calli Nguyen is ok/needs improvement
i-clicker-3
A. Jack Owen is very good
B. Jack Owen is ok/needs improvement
C. Zach Vance is very good
D. Zach Vance is ok/needs improvement
i-clicker-4
A. Brad Goetz is very good
B. Brad Goetz is ok/needs improvement
Chapter 9.2 Announcements:
Homework 9.2: due Thursday, April 1, in class (Calli Nguyen)
Exercises: 9, 10, 11, 12, 14, 15, 16, 23, 24, 31, 32
Problems: 1, 2, 3, 4
- Remember: Homework 9.1 is due Thursday, March. 25, in class
Heads up: Midterm 2 is coming up on April 13
We’ll now cover only parts of each chapter (let me know if you want me to cover something that is not
on the list and that interests you):
- 5.1 Balloons
- 11. Household Magnets & Electric Motor
- 7.1 Woodstoves
- 11.2 Electric Power Distribution
- 9.1 Clocks, harmonic oscillation
- 15.1. Optics, cameras, lenses
- 9.2 Musical Instruments, waves
- 16.1 Nuclear Weapons
- 10.3 Flashlights
Chapter 9.2
Musical Instruments (waves)
Concepts
Demos and Objects
-
waves in a room/stadium
waves in a pipe
a speaker (creating sound)
ear
tuning fork
waves on a string
wave modes (harmonics)
-
longitudinal waves
transverse waves
traveling & standing waves
waves on a string
waves in an air column
ear and hearing
wave length
frequency/pitch
sound
Traveling transverse waves
Crest/bump travels
Transverse waves:
Transverse waves:
particle
wave
The particles of the
disturbed medium
move perpendicular
to the wave motion
Traveling, longitudinal waves
compression travels
Longitudinal waves:
Longitudinal waves:
The particles of the
disturbed medium move
parallel to the wave
motion
Examples of waves (i-clicker-1):
Which wave is a longitudinal wave?
A. “Bump” traveling down a string:___________________
B. Sound waves:____________________
C. La ola in a stadium (getting up/sitting down):_____________
D. Water wave: ____________________________
Basic Variables of
Wave Motion
Terminology to describe
waves
- Crest: “Highest point” of a wave
- Wavelength l: Distance from one crest to the next crest.
- Wavelength l: Distance between two identical points on a wave.
- Period T: Time between the arrival of two adjacent waves.
- Frequency f: 1/T, number of crest that pass a given point per unit time
Sound
- is a wave (sound wave)
- Rarefied and compressed regions
- Longitudinal wave
- air molecules move back and forth
Sound Waves
Sound waves are longitudinal waves.
They consist of compressed and rarified regions of gas (medium)
We can hear (audible) frequencies from about 20 Hz (low) to 15,000 Hz (high).
Infrasonic “sound” waves: below ~ 20 Hz
Ultrasonic sound waves: above ~ 15,000 Hz
The speed of sound in air: c ~ 343 m/s ~ 740 mi/hr ~ 0.2 mi/sec. (dry air, 68F)
i-clicker-2
It is a dark and stormy night.
Lightning strikes in distance.
You see the lighting, then, after
ten seconds you hear the
thunder.
How far away did the lighting
strike?
A. 1 mile
B. 2 miles
C. 3 miles
D. 4 miles
E. 5 miles
Sound waves, hearing and the ear
http://www.innerbody.com/anim/ear.html
Notes and their
fundamental
frequency
Octaves: frequency
doubles for each tone
Creating standing waves:
When two waves are traveling back and forth, under the
right conditions (right frequency), we can create standing
waves.
Standing waves have stationary nodes and antinodes
Examples we’ll talk about:
- Standing waves on a string.
- Standing waves in a pipe (open and closed).
String Harmonics
frequency
L
1 T
f1 
2L m
2f1
3f1
4f1
5f1
6f1
L … Length of string;
T … Tension
m … mass of string
Standing waves have stationary
nodes and anti-nodes
1 T
f1 
2L m
L … Length of string
T … Tension (not period T)
m … mass of string
Strings as Harmonic Oscillators
• A string is a harmonic oscillator
–
–
–
–
Its mass gives it inertia
Its tension gives it a restoring force
It has a stable equilibrium
Restoring forces are proportional to displacement
• Stiffness of restoring forces determined by
– String’s curvature
– String’s tension
Fundamental Vibration
• String vibrates as a single arc, up and down
– velocity antinode occurs at center of string
• This is the fundamental vibrational mode
• Pitch (frequency of vibration) is
– proportional to tension
– inversely proportional to string length
– inversely proportional to mass
1 T
f1 
2L m
i-clicker-3
How can a violin player play a lower note:
A.Increasing the tension in the string.
B.Playing a string with less mass (thinner string).
C.Shortening the string.
D.A & C
E.None of the above.
Overtone Vibrations
• In addition, string can vibrate as
– two half-strings
– three third-strings
– etc.
• These are higher-order vibrational modes
• These modes have higher pitches – overtones
Harmonics in a String
• In a string, the overtone pitches are
– two times the fundamental frequency (octave)
– three times the fundamental frequency
– etc.
• These integer multiples are called harmonics
• Bowing or plucking a string tends to excite a
mixture of fundamental and harmonic
vibrations, giving character to the sound
notes
E5
A4
D4
G3
i-clicker-4:
Why do all musical instruments have a body
(wood body, metal shell, etc)?
A.They look prettier
B.They are easier to hold
C.They act as resonators (amplify sound)
D.They act as dampers (reduce sound)
E.No good reason
Music and Resonance:
Primary and secondary oscillators
strings
body
Mouthpiece
Air column
String Instruments
Wind Instruments
Connecting primary (strings) and
secondary (body) oscillators
Producing Sound
• Thin objects don’t project sound well
– Air flows around objects
– Compression and rarefaction is minimal
• Surfaces project sound much better
– Air can’t flow around surfaces easily
– Compression and rarefaction is substantial
• Many instruments use surfaces for sound
Violin Harmonics
Viola Harmonics
Compare to Chladni plate demo
i-clicker-5:
Why are some violins so expensive (Stradivarius : $ 1.5 M)?
Computer Tomography scan of
a Nicolo Amati Violin (1654)
A.
B.
C.
D.
E.
Old stuff is always expensive.
They are made of expensive materials.
In fashion and music, you pay for the label.
The secondary oscillator mixes a rich sound of harmonics.
The primary oscillator produces unusual frequencies.
Primary Resonators: Wind Instruments
Flute
Woodwinds
Brass
Lips
Fixed Edge
Reed
Open pipe:
Fund. Frequency
f1  1 
c
2L
f2  2 
c
2L
f3  3 
c
2L
c
f1 
2L
c… speed of sound
c = 343 m/s in air
Half-closed pipe:
Fundamental
frequency:
c
f1  1 
4L
c
f2  3 
4L
c
f3  5 
4L
i-clicker-6; 7:
You play an open organ pipe with a length of 1m.
What is the fundamental frequency?
A.1 Hz
B.86 Hz
C.172 Hz
D.343 Hz
E.686 Hz
Now you close the pipe at one end. What will the frequency be then?
A.1 Hz
B.86 Hz
C.172 Hz
D.343 Hz
E.686 Hz
Air as a Harmonic Oscillator
• A column of air is a harmonic oscillator
–
–
–
–
Its mass gives it inertia
Pressure gives it a restoring force
It has a stable equilibrium
Restoring forces are proportional to displacement
• Stiffness of restoring forces determined by
– pressure
– pressure gradient
Fundamental Vibration
• Air column vibrates as a single object
– Pressure antinode occurs at center of open column
– Velocity antinode occurs at ends of open column
• Pitch (frequency of vibration) is
– inversely proportional to column length
– inversely proportional to air density
• A closed pipe vibrates as half an open column
– pressure antinode occurs at sealed end
– Velocity node occurs at the sealed end
– frequency is half that of an open pipe
Harmonic Vibrations
• In addition, column of air can vibrate as
– two half-columns
– three third-columns
– four fourth-columns
• These higher-order modes are the harmonics
• Pitches are integer multiples of the fundamental
• Blowing across column tends to excite a mixture
of fundamental and harmonic vibrations