Standing Waves • Waves that reflect back and forth interfere. • Some points are always at rest – standing waves.
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. node antinode
Harmonics • The lowest frequency that can fit is the fundamental frequency. • Higher frequencies are called harmonics.
Percussion instruments strike an object with an impulsive force. The object oscillates with a fundamental frequency (pitch) and harmonics. Bulk modulus Mass density Percussion F
Strings • String instruments use friction to cause a resonant oscillation. • The frequency is controlled on the instrument string. • Length • Tension • Mass density v Ffr
Columns of air can be directly vibrated. Displacement is maximum at the open end. Where displacement is maximum, pressure is minimum. Open Ends
One end open and one end closed creates a different set of harmonics. These patterns are the basis for wind instruments. Single End
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 Clarinet next