Musical Acoustics

How do wind instruments like flutes, saxophones, and trumpets produce sounds?

In wind instruments the column of air is the oscillating object. The musician must create the oscillation. Perhaps you have blown over the top of a soda bottle and created a tone. When you blow some of the air goes into the bottle. That increased air pressure is reflected off the bottom of the bottle and returns to the top where it deflects the blown air upward. This process repeats, resulting in a tone whose frequency depends on the length of the bottle. The energy in your breath is converted into the energy of oscillation of the air in the bottle.

A flute works in a similar way, where the player blows over a hole in the side of the flute. The other end of the flute is open. The sound wave is reflected because the impedance in the tube is different from that of the room air. The spectrum of a flute contains all harmonics. If the player blows harder and changes the location of her top lip she can make the flute play one or two octaves higher. In other words, the fundamental frequency of the flute is increased by a factor of two or four.

The frequency of a flute or other woodwind instrument can be changed by opening holes along the side of the instrument. This shortens the length of the oscillating air column, increasing the frequency.

In a saxophone or clarinet the vibrations are caused by a thin piece of wood called the reed. The player blows through a gap between the reed and the instrument’s mouthpiece. The pulse of air is reflected off the end of the instrument and returns to the reed, pushing it open to admit another pulse of air. Double-reed instruments like the oboe and bassoon work in the same way. The clarinet is shaped like a cylinder. Its spectrum consists of only the odd harmonics: 1, 3, 5, and 7, etc. A clarinet can be played in a higher register by opening a small hole near the mouthpiece that strongly reduces the amplitude of the fundamental tone. The new pitch is an octave and a fourth higher than the lower register. Saxophones are not shaped like cylinders, but like cones. As a result all harmonics are included in its spectrum, and opening the register key raises the instrument’s pitch by one octave.

In a bugle, trumpet, trombone, French horn, or other brass instrument the oscillations are caused by the player’s lips. The lips act as a valve, causing pulses of air into the instrument, which causes the oscillations in the air column. In a brass instrument the fundamental tone is absent. By adjusting the tightness of the lips the player can cause the instrument to play at the 2nd, 3rd, 4th harmonic, etc. The valves on a brass instrument add small lengths of tubing, lowering the pitch. In a trombone the length of the tube can be varied continuously, allowing any frequency to be played. The spectrum of a brass instrument depends strongly on its pitch and loudness. The louder it is played, the more energy there is in the higher harmonics.

Some synthesizers like this one use keyboards to select the sound to be generated, while others use computers. The ability of a synthesizer to immitate various instruments is accomplished using frequency modulated synthesis to create “voices.”

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