Musical InstrumentsMusical Instruments

Standing WavesStanding Waves

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

Closed EndsClosed Ends

Both ends fixed limits the Both ends fixed limits the standing wave.standing wave.

A whole number of half-A whole number of half-wavelengths must fit in wavelengths must fit in the space.the space.

A whole number of A whole number of nodes nodes and and antinodesantinodes..

node antinode

HarmonicsHarmonics

The lowest frequency that can fit is the The lowest frequency that can fit is the fundamentalfundamental frequency. frequency.

Higher frequencies are called Higher frequencies are called harmonicsharmonics..

PercussionPercussion

Percussion instruments Percussion instruments strike an object with an strike an object with an impulsive force.impulsive force.

The object oscillates with a The object oscillates with a fundamental frequency fundamental frequency (pitch) and harmonics.(pitch) and harmonics.• Bulk modulusBulk modulus

• Mass densityMass density

F

StringsStrings

String instruments use String instruments use friction to cause a resonant friction to cause a resonant oscillation.oscillation.

The frequency is controlled The frequency is controlled on the instrument string.on the instrument string.• LengthLength

• TensionTension

• Mass densityMass density

vFfr

Open EndsOpen Ends

Columns of air can be Columns of air can be directly vibrated.directly vibrated.

Displacement is maximum at Displacement is maximum at the open end.the open end.

Where displacement is Where displacement is maximum, pressure is maximum, pressure is minimum.minimum.

Single EndSingle End

One end open and one end One end open and one end closed creates a different set closed creates a different set of harmonics.of harmonics.

These patterns are the basis These patterns are the basis for wind instruments.for wind instruments.

ClarinetClarinet

The clarinet has an air The clarinet has an air column 32.8 cm long and act column 32.8 cm long and act like a column open at one like a column open at one end.end.

What is the fundamental What is the fundamental frequency?frequency?

The first harmonic isThe first harmonic is

The speed of sound is 343 The speed of sound is 343 m/s.m/s.• f = (343 m/s) / 4 (0.328 m)f = (343 m/s) / 4 (0.328 m)

• f = 261 Hzf = 261 Hz

Lvf

L

4/

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