Standing Waves: Modes of Oscillation and Overtone Series

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The Week Ahead…
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Mon: Waves on stringed instruments (lab 4)
Tues: Oscillations in wind instruments (lab 5)
Wed: No class; work on your labs and hw assignment
Thur: Harmonic Series Analysis (lab 6)
Fri: Fun demos!
DUE DATES:
Labs 4 and 5 due Friday at beginning of class.
HW 1 due Friday, 5pm
Standing Waves: Modes of
Oscillation and Harmonic Series
Phys/Mus 102
Spring 2014
Resonance
Every oscillating system has a natural frequency.
Force on object occurs exactly in phase with the displacement,
leading to a “build up” of maximal displacement.
Key terms
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Resonance
Reflection, fixed end, free end
Superposition
Standing wave
Node/anti-node
Harmonic series
Mersenne’s Law
Chladni pattern
Reflection
Hard Boundary/Fixed End
Phase change!
Soft boundary/Free End
 No phase change
Standing Waves
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Result from superposition of incident waves and reflected
waves
Only certain wavelengths/frequencies are allowed!
Harmonic Series
f1, 1st harmonic
(fundamental)
f2, 2nd harmonic
f3, 3rd harmonic
A few more in the series…
Question: What will you hear if you touch your finger to the middle of the string?
The overtone series notes
Mersenne’s Law
f1 = fundamental frequency
L = length of string
T = tension in string
m = mass per unit length of string
Mersenne’s Law Generalized
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Nth harmonic occurs at
frequency:
N = 1 = first harmonic
N = 2 = second harmonic
N = 3 = third harmonic
…
Chladni Patterns
What happens with
more complex objects:
Pianos, Drums, Guitars,
Violins, etc?
Modes on Guitar String
More Chladni Patterns (Guitar!)
Instruments with complex structures have harmonic series/
resonance frequencies too!
Guitar Bracing
Chladni Patterns (Drums!)
Animations courtesy of Dan Russel, Kettering University.
Piano soundboard modes
Chladni Patterns (Violin!)
Image/Animation Sources
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http://www.foreverparenting.com/1336/summer-fun-now-with-more-learning/
http://www.maestromindsguitarschool.com/guitar_website/Tools%20and%20Articles/guide
_to_buying_your_first_guitar.html
http://hep.physics.indiana.edu/~rickv/Standing_Waves_on_String.html
http://www.animations.physics.unsw.edu.au/waves-sound/standing-waves/index.html
Berg and Stork, Physics of Sound, 3rd ed.
http://www.phys.unsw.edu.au/~jw/guitar/guitarchladni_engl.html
http://vanadium.rollins.edu/~tmoore/piano_soundboard.htm
http://www.speech.kth.se/music/5_lectures/conklin/howdoes.html
http://thecraftsmanspath.com/2008/04/06/dreadnought-guitar-bracing-the-top/
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