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The Week Ahead…

The Week Ahead…. 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.

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The Week Ahead…

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  1. The Week Ahead… 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

  2. Standing Waves: Modes of Oscillation and Harmonic Series

    Phys/Mus 102 Spring 2014
  3. 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.
  4. Key terms Resonance Reflection, fixed end, free end Superposition Standing wave Node/anti-node Harmonic series Mersenne’s Law Chladni pattern
  5. Reflection Hard Boundary/Fixed End Phase change! Soft boundary/Free End  No phase change
  6. Standing Waves Result from superposition of incident waves and reflected waves Only certain wavelengths/frequencies are allowed!
  7. Harmonic Series f1, 1st harmonic (fundamental) f2, 2ndharmonic f3, 3rdharmonic
  8. A few more in the series… Question: What will you hear if you touch your finger to the middle of the string?
  9. The overtone series notes
  10. Mersenne’s Law f1= fundamental frequency L = length of string T = tension in string m = mass per unit length of string
  11. Mersenne’s Law Generalized Nth harmonic occurs at frequency: N = 1 = first harmonic N = 2 = second harmonic N = 3 = third harmonic …

  12. Chladni Patterns

    What happens with more complex objects: Pianos, Drums, Guitars, Violins, etc?
  13. Modes on Guitar String
  14. More Chladni Patterns (Guitar!) Instruments with complex structures have harmonic series/ resonance frequencies too!
  15. Guitar Bracing
  16. Chladni Patterns (Drums!) Animations courtesy of Dan Russel, Kettering University.
  17. Piano soundboard modes
  18. Chladni Patterns (Violin!)
  19. Image/Animation Sources 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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