150 likes | 452 Vues
Musical Instruments. 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.
E N D
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 acts 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
The sound from a source reaches each ear at a separate time. Brain uses the time difference to tell direction. Hard with short wavelength. Stereo speakers reconstruct timing differences. Constructive and destructive interference Speaker Systems
Beats • When two wavelengths are at nearly the same frequency the superposed waves create beats. The separation of peaks is the period T = 1 / f The difference in frequencies is the beat frequency Df. The beat period T = 1 / Df.
A 440 Hz-tuning fork is held near a vibrating piano string. The tuner hears 20 beats in 5 s. What is the pitch of the piano string? Will the tuner ever get it tuned perfectly? The beat frequency is 20 beats / 5 s = 4 Hz. The piano string could be either at 444 or 436 Hz. Note: a beat period of 1 min would get a frequency accurate to 0.016 Hz. In Tune