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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.

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## Musical Instruments

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**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

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