1. The Physics of Music
Waves

2. Sources of Sound
As we learned yesterday, sound is produced by a vibrating object.
Reed instruments (clarinet, saxophone, etc.) have a wooden reed that vibrates as air passes by it.
For brass instruments (tuba, trumpet, etc.), it is the lips of the person playing the instrument that vibrate.

3. Resonance in Air Columns
Closed-pipe resonator
A resonating tube with one end closed.
The sound wave will reflect back up off of a closed surface.
Open-pipe resonator
A resonating tube with both ends open.
The sound wave will reflect back up off of an open surface.

4. Resonance in Air Columns
Resonance lengths
A standing sound wave in a pipe can be shown using a sine wave, that represent either the air pressure or the displacement of the air particles.
These standing waves have nodes and antinodes.
Pressure – the nodes are regions of mean pressure and the antinodes are regions of high or low pressure
Displacement – the nodes are regions of low displacement and the antinodes are regions of high displacement

5. Resonance in Air Columns
Resonance frequencies in a closed pipe
The shortest column of air that can have an antinode at the closed end and a node at the other is one-fourth of a wavelength long.
Additional resonant frequencies occur every ½ wavelength.
λ/4, 3λ/4, 5λ/4, etc.

6. Resonance in Air Columns
Resonance frequencies in an open pipe
The shortest column of air that can have nodes at both ends is one-half of a wavelength long.
Additional resonant frequencies occur every ½ wavelength.
λ/2, λ, 3λ/2, etc.

7. Resonance on Strings
Because a string on an instrument is clamped on both ends, it must have nodes at each end.
Resonance frequencies occur at λ/2, λ, 3λ/2, 2λ, etc.
The tighter the string, the faster the wave moves along it, therefore the higher the frequency.

8. Sound Quality A tuning fork produces a single, pure sound.
The human voice, a clarinet, and other instruments do not.
They have many frequencies that are added together to produce “one” sound.
The difference between two is called timbre (tone color, tone quality).

9. The Sound Spectrum
Fundamental – the lowest frequency that resonates for an instrument. Also called the first harmonic.
Harmonics – odd-number multiples of the fundamental frequency.

10. Consonance and Dissonance
Dissonance – an unpleasant set of pitches
Consonance – a pleasant combination of pitches
Different cultures have different definitions of what is defined to be pleasant.

11. Beats Interference is the interaction of two or more waves.
Beats – the periodic fluctuation in the loudness of sound due to the interference of two sound waves.