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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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Musical instruments l.jpg

Musical Instruments


Standing waves l.jpg

Standing Waves

  • Waves that reflect back and forth interfere.

  • Some points are always at rest – standing waves.


Closed ends l.jpg

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 l.jpg

Harmonics

  • The lowest frequency that can fit is the fundamental frequency.

  • Higher frequencies are called harmonics.


Percussion l.jpg

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 l.jpg

Strings

  • String instruments use friction to cause a resonant oscillation.

  • The frequency is controlled on the instrument string.

    • Length

    • Tension

    • Mass density

v

Ffr


Open ends l.jpg

Columns of air can be directly vibrated.

Displacement is maximum at the open end.

Where displacement is maximum, pressure is minimum.

Open Ends


Single end l.jpg

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

These patterns are the basis for wind instruments.

Single End


Clarinet l.jpg

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

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