Understanding Standing Waves in Music Theory

1. Music

2. Standing Waves • At the right frequencies a constrained wave will produce a standing wave • Standing waves appear stationary • Result of constructive and destructive interference • Have nodes and antinodes

3. Nodes and Antinodes • Nodes • Wave doesn’t move • Destructive interference • Antinodes • Wave moves • Constructive interference

4. Harmonics • Fundamental frequency • Two nodes • Half a wavelength in between ends • Pattern of standing waves is called the harmonic series

5. Harmonic Series • String or pipe open at both ends • n = 1, 2, 3, 4, … • String – both ends are nodes • Open pipe – both ends are antinodes • Pipe closed at one end • n = 1, 3, 5, … • Pipe open at one end – closed side in node, open side in antinode

6. Instruments • Vibrating strings • Violins, guitars, bass etc. • Piano, harpsichord • Pipe open at both ends • Flute • Pipe open at one end and closed at the other • Saxophone, clarinet, trumpet, trombone, etc.

7. Timbre • Different instruments playing the same note sound different because of harmonics • The intensity of the harmonics varies between instruments • Changes the timbre, or sound quality of each instrument

8. Beats • When two waves of different frequencies interfere the result is a complex interference pattern • The result is areas of constructive interference and areas of destructive interference • This amplitude variation are the beats • And the frequency with which they vary is the beat frequency • Beat frequency is the difference between the original two waves frequency

9. Consonance and Dissonance • Depends on the frequency difference between two tones • Varies between cultures and eras • Consonance • Octave • Perfect fourth • Perfect fifth • Dissonance • Minor second • Major seventh