1. Musical Instruments

2. Standing Waves  Waves that reflect back and forth interfere.  Some points are always at rest – standing waves.

3. Closed Ends  Both ends fixed limits the standing wave.  A whole number of half- wavelengths must fit in the space.  A whole number of nodes and antinodes. nodeantinode

4. Harmonics  The lowest frequency that can fit is the fundamental frequency.  Higher frequencies are called harmonics.

5. Percussion  Percussion instruments strike an object with an impulsive force.  The object oscillates with a fundamental frequency (pitch) and harmonics. Bulk modulusBulk modulus Mass densityMass density F

6. Strings  String instruments use friction to cause a resonant oscillation.  The frequency is controlled on the instrument string. Length Tension Mass density v F fr

7. Open Ends  Columns of air can be directly vibrated.  Displacement is maximum at the open end.  Where displacement is maximum, pressure is minimum.

8. Single End  One end open and one end closed creates a different set of harmonics.  These patterns are the basis for wind instruments.

9. Clarinet  The clarinet has an air column 32.8 cm long and act like a column open at one end.  What is the fundamental frequency?  The first harmonic is  The speed of sound is 343 m/s. f = (343 m/s) / 4 (0.328 m) f = 261 Hz next