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 f 1, 1 st harmonic (fundamental) f 2, 2 nd harmonic f 3, 3 rd harmonic

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 f 1 = fundamental frequency L = length of string T = tension in string  = 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. What happens with more complex objects: Pianos, Drums, Guitars, Violins, etc? Chladni Patterns

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://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, 3 rd 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/