Standing Waves and the Overtone Series

1. Standing Waves and the Overtone Series Standing Waves: Transverse-Stringed Instruments and Longitudinal-Wind Instruments

2. Longitudinal Standing Waves Musical instruments in the wind family depend on longitudinal standing waves in producing sound. Since wind instruments (trumpet, flute, clarinet, pipe organ, etc.) are modified tubes or columns of air, it is useful to examine the standing waves that can be set up in such tubes.

3. Phase Change during reflection

4. Open tube of air A pictorial representation of longitudinal standing waves on a Slinky (left side) and in a tube of air (right side) that is open at both ends (A, antinode; N, node).

5. Closed tube of air A pictorial representation of the longitudinal standing waves on a Slinky (left side) and in a tube of air (right side) that is open only at one end (A, antinode; N, node).

7. Clarinet The clarinet is an example of a cylindrical bore instrument closed at one end. Because of this, the normal resonant modes must have an air displacement minimum at the closed end (the mouthpiece) and an air displacement maximum near the first end key or the bell. These conditions result in the presence of only odd harmonics in the sound. This contrasts from the saxophone or oboe, which have a conical bore and include the even harmonics. The absence of even harmonics is part of what is responsible for the “warm” or “dark” sound of a clarinet compared to the “bright” sound of a saxophone.

8. 3.5 Other Standing Waves and Applications • Drumhead • Chladni Plate • Tacoma Narrows Bridge

9. Vibrational Modes of a Circular Membrane (Drumhead) • http://www.kettering.edu/~drussell/Demos/MembraneCircle/Circle.html

10. Chladni Figures and Vibrating Plates • http://www.phy.davidson.edu/StuHome/jimn/Java/modes.html

11. The Collapse of the Tacoma Narrows Bridge • http://www.youtube.com/watch?v=3mclp9QmCGs