1. Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency of the system, the system is said to be in resonance

2. Standing Waves When an incident wave interferes with a reflected wave to form areas of constructive and destructive interference. Nodes are where the resulting wave remains stationary. Anti-nodes are where the resulting wave has max amplitude.

3. Other Examples of Resonance Child being pushed on a swing Shattering glasses Tacoma Narrows Bridge collapse due to oscillations by the wind Upper deck of the Nimitz Freeway collapse due to the Loma Prieta earthquake

4. 1989 Loma Prieta earthquake Aka Quake of '89 World Series Earthquake

5. Resonance Resonance: a vibration of large amplitude in a mechanical or electrical system caused by a relatively small periodic stimulus of the same or nearly the same period as the natural vibration period of the system. http://www.merriam-webster.com/dictionary/resonance

6. How many wavelengths? 1 2 1 ½ ½

7. How does a Guitar String Vibrate? ½  = L = 2L L

8. What is the velocity of the wave on the string? v = f = 2L

9. Different Frequencies How can I change the frequency (note)?

10. Harmonics! When you sound the guitar note, you hear other frequencies.

11. How does a Guitar String Vibrate?

14. Fundamental frequency 2 nd Harmonic 3 rd Harmonic 4 th Harmonic = 2L f 2 = v/L f 3 = 3v/2L f 4 = 2v/L f 1 = v/2L = L = 2/3 L = ½ L

15. Summary f = nv/2L n is the # of antinodes or harmonic Fundamental Frequency is the LOWEST frequency All harmonics are multiples of the fundamental frequency (e.g. f 1 = 50 hz, then f 2 = 100 hz, f 3 = 150 hz, etc) = 2L/n

16. Fundamental frequency 1 st Harmonic 2 nd Harmonic 3 rd Harmonic 4 th Harmonic How does a Guitar String Vibrate?