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Science Olympiad

Sounds of Music Event

Important Fundamental Concepts in Musical Acoustics

1. Harmonic Series and its relationship to Harmony

    A. Numbers in a harmonic series have a 1, 2, 3, ... relationship
    B. Example: Harmonics of 440: 440, 880, 1320, 1760, 2200, ....
    C. Example: Pitch sequence C4, C5, G5, C6, E6, G6, flat Bb6, C7, ...(bugle calls)
    D. Consonant intervals: 2/1 = P8 (octave), 3/2 = P5 (fifth), 4/3 = fourth P4, 5/4 = third M3

2. Wave theory

    A. Longitudinal (compressional) waves in air
    B. Transverse waves in strings
    C. Bending waves (combination of other two) in stiff bars
    D. Higher frequency --> Shorter wavelength
    E. Higher wave speed --> Longer wavelength
    F. In 2 or 3 dimensions, waves spread out from source, get smaller in amplitude

3. Resonance in simple oscillators (spring/mass)

    A. Spring provides restoring force, brings mass back to center "equilibrium position"
    B. Mass provides inertia, keeps moving past equilibrium position
    C. Stiffer spring (2 side-by-side, or 1 shorter spring) increases frequency
    D. Larger mass (inertia) reduces frequency
    E. Stretched or compressed spring --> Potential energy
    F. Moving mass --> Kinetic energy

4. Wind instruments

    A. Longer tube --> longer wavelength --> lower frequency
    B. Larger hole --> air can rush in and out faster --> higher frequency
    C. In bottle instruments, cavity acts like spring, smaller cavity --> stiffer spring --> higher f.
    D. Frequency f proportional to 1/(Tube length L), so 1 octave lower is 2x longer

5. String instruments

    A. Longer string --> longer wavelength --> lower frequency, f proportional to 1/L
    B. Higher tension --> greater restoring force --> higher frequency
    C. Heavier string --> greater mass (inertia) --> lower frequency
    D. Thin string doesn't radiate well, instead energy --> bridge --> body --> room
    E. Thinner top plate --> more motion --> louder
    F. Cavity + Hole like a bottle --> tune bottle for louder sound

6. Xylophone instruments

    A. Longer bar --> longer wavelength --> lower frequency, now f proportional to (1/L)^2
    B. Removing material can remove moving mass (on free end) or stiffness (where bending)
    C. Careful! Long, thin bars don't radiate well at low frequencies! LISTEN to scale!

Peter Hoekje
Associate Professor of Physics
Department of Physics
Baldwin-Wallace College
Berea, OH 44017
(440) 826-2494
phoekje@bw.edu

Professional Interests
Musical Acoustics
Physics Education