Standing Waves: Modes of Oscillation and Harmonic Series Phys/Mus 102 Spring 2015.
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Transcript of Standing Waves: Modes of Oscillation and Harmonic Series Phys/Mus 102 Spring 2015.
Standing Waves: Modes of Oscillation and Harmonic Series
Phys/Mus 102
Spring 2015
Resonance
Every oscillating system has a set of natural frequency, the frequencies at which the system “wants” to vibrate.
Key terms
Resonance Reflection, fixed end, free end Superposition Standing wave Node/anti-node Harmonic series Mersenne’s Law Chladni pattern
Reflection
Hard Boundary/Fixed EndPhase change!
Soft boundary/Free End No phase change
Standing Waves and Modes
Result from superposition of incident waves and reflected waves Only certain combinations of wavelengths and frequencies allowed!
= Mode
Harmonic Series
f1, 1st harmonic (fundamental)
f2, 2nd harmonic
f3, 3rd harmonic
A few more in the series…
Question: How can you excite mode or prevent certain ones?
Overtone series
At which frequencies do these modes occur?
What physical variables matter?
Mersenne’s Law
f1 = fundamental frequency
L = length of stringT = tension in stringm = mass per unit length of stringMarin Mersenne
Mersenne’s Law Generalized
Nth harmonic occurs at frequency:
N = 1 = first harmonicN = 2 = second harmonicN = 3 = third harmonic…
Superposition of Modes
Modes on Guitar String
What happens with more complex objects: Pianos, Drums, Guitars, Violins, etc?
Chladni Patterns
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!)
Resources and Citations
http://newt.phys.unsw.edu.au/jw/strings.html
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/