DHC 161 2/28/12

1. DHC 1612/28/12 Energy input strategies Interaction between source and standing wave

2. Essential Features Review • Medium to support standing waves • Harmonic series  definite pitch • most common: strings or air-filled tubes • Energy input strategy • Create (and sustain) the standing waves • Amplification strategy • Strings require a soundboard and/or resonator • Wind instruments typically have a horn • Pitch changing strategy • Almost always change the length of vibrating medium • Practical to play • Problem of finger holes being too far apart

3. Strategies for sustaining standing waves Almost contradictory requirements • Allow the medium to vibrate freely at its many natural frequencies • Stimulate the standing waves that make those frequencies Solutions Use a method of “pushing” the medium that readily adapts to the standing wave frequencies Also make use of the fact that abrupt or discrete pulses generate many harmonics automatically

4. stick-slip Bowed instruments Natural stick-slip frequency that depends on friction, applied force, and the relative motion of bow & string. Feedback The stick-slip frequency will adjust to the frequency of the string’s vibration.

5. Feedback Interaction between the standing waves and the energy source The source of vibration is usually weak and subtle. It is easily influenced by the motion of the medium, itself. The source will adjust its own frequency to match the natural frequency of a standing wave (usually the fundamental). This adjustment & growth happens during the attack.

6. Vibrating reed single reeds double reeds Reeds oscillate due to blowing: • Air flow between reeds causes gap to close (Bernoulli effect) • Restoring force of bent reeds causes gap to open again Feedback Pressure pulses from oscillating reeds are reflected from the end of the tube, travel back to the reed opening, and influence the opening and closing of the gap.

7. Buzzing lips Lips act like a pair of reeds • Air flow through small gap between lips causes lips to close. • Air being pushed from lungs forces lips open again. • Feedback process is same as for reeds, but performer has more control over lip tension than with reeds.

8. Edge tone Air blown past an edge naturally oscillates (vortex shedding) flutes recorders some organ pipes pan pipes Feedback If the edge is part of a tube, reflected pressure pulses will influence the timing of vortex shedding

9. Transient sound • Amplitude decays for two main reasons • Friction within vibrating medium and with air • Sound radiates energy away • Examples: • Plucked string • Tapped plate or membrane (drumhead) • Tapped tube of air • Handclap (sound comes from sudden change of air pressure, which happens only once)

10. Sustained sound Regardless of the input mechanism, energy needs to be continually applied to the vibrating medium to replace energy that is “leaking” out • Rate of energy applied is less than rate of energy leaked - vibration (and sound) amplitude will decrease 2) Rate of energy applied is equal to rate of energy leaked - amplitude will stay constant 3) Rate of energy applied is greater than rate of energy leaked - amplitude will increase

11. Energy in = Energy out Most vibrating systems – including musical instruments – will reach a stable amplitude for a given amount of energy input. Such behavior is called self-limiting. Why does this happen? The rate of energy loss is proportional to amplitude. The faster and farther a string moves, the more work it does against the air (creating sound and friction) Regardless of the level of energy input, the amplitude will grow until the rate of energy loss equals the rate of energy applied. The growth phase of a note played on a musical instrument is usually referred to as the attack

12. The Attack The beginning of a sustained note during which... synchronicity between vibration source and standing waves has not yet been established the amplitude of standing waves is still growing