1. Resonance Chapter 4

2. Concert Talk

3. Resonance: definition When a vibrating system is driven by a force at a frequency near the natural frequency of the system, a relatively large amplitude results.

4. Resonance of Mass-Spring Vibrator Natural frequency of the system (determined by frequency equation) Drive the system with a crank at any frequency When frequency of crank and natural frequency match, amplitude will build to maximum.

5. Linewidth and Q Amplitude builds to max and decreases symmetrically around ƒ 0. Linewidth (∆f ) is measured at an amplitude of 0.707 (71%) of A max. 0.707 is 1 divided by the square root of 2. Q = f 0 /∆f

6. Phase Position in the cycle of a vibration Phase Difference: A comparison between the positions of two vibrating objects at the same time, or The relative position in a vibration cycle, of a vibrating object and a driving force.

7. Standing Waves on a String Constructive and destructive interference leads to standing waves Fig. 4.5 compares modes of vibration with wavelength on a string (fixed at both ends) Frequency of nth mode will be n times the frequency of the first mode.

8. Wave Speed in Wire or Spring Transverse Wave:

9. Partials, Harmonics, Overtones Partials include all modes of vibration, including the fundamental. Overtones are all partials above the fundamental. Harmonics refer to modes of vibration that are integer-related (or nearly integer-related), including the fundamental.

10. Open and Closed Pipes Open end of a pipe behaves like the fixed end of a string. pulse reflects with opposite displacement Open pipe acts like a string fixed on both ends, wavelength = 2L. Closed end of pipe reflects pulses with same displacement. Wavelength = 4L. Only odd-numbered harmonics are present.

11. Pipe Recipes Open Pipe: Closed Pipe:

12. End Correction for Pipes Pressure drops to zero a small distance beyond open end of pipe End Correction = 0.61r Add to both ends of open pipe to find its acoustic length. Add to one end of closed pipe to find its acoustic length.

13. Acoustic Impedance Defined as the ratio of sound pressure to volume velocity, measured in acoustic ohms. Most important to note that it varies inversely to surface area, so that changes in diameter, or the addition of a cross-branch to a tube, will cause reflections in sound waves.