1. Standing waves and Normal modes Lecture 7 Pre-reading : §16.1

2. Standing Waves Formed through reflection + superposition of waves moving in opposite directions Contains ‘nodes’ (no displacement) and ‘anti-nodes’ (maximum displacement) “Normal Mode”: property of a system in which all particles move sinusoidally at same freq. Lowest freq. normal mode: ‘fundamental’ Higher freq. normal modes: ‘harmonics’/‘overtones’ §15.8

3. Longitudinal Waves Displacement is in direction of wave motion Need to distinguish particles from pressure §16.1

4. Three ways to describe sound waves Pressure is 90 0 out of phase with displacement! Sound as Pressure Wave

5. Longitudinal Standing Waves Waves reflect at open or closed end Need to distinguish displacement of particles from pressure Node: no displacement Anti-node: Time-averaged location where max displacement is reached Displ. node = Pressure anti-node Displ. anti-node = Pressure node

6. Open pipesClosed pipes f n = n  / (2 L ), n = 1, 2, 3, … f n = n  / (4 L ), n = 1, 3, 5, … §16.4

7. Interlude: Musical instruments Musical instruments use the properties of normal modes to make music. Instrument design ⇒ allow players to produce note of desired frequency

8. One oscillator

9. Last Post

10. fnote f1f1 65 HzC2C2 f2f2 130 HzC3C3 f3f3 195 HzG3G3 f4f4 260 HzC4C4 f5f5 325 HzE4E4 f6f6 390 HzG4G4 f7f7 455 HzB♭4B♭4 f8f8 520 HzC5C5...etc ear interprets ratio of frequencies as intervals, e.g. f 2 : f 1 = 2 ⇒ octave f 2 : f 1 = 1.5 ⇒ fifth etc.

11. One oscillator per note

13. pressing fingers on fingerboard changes length of string ⇒ frequency f Changing the length of the oscillator

14. fingerholes change length of pipe speaker hole (thumb hole) forces 2nd harmonic

15. Trombone tube is about 275cm long.

16. To get other notes: add slide add valves All designed to increase length of pipe ⇒ increase wavelength λ

17. Clarinet

19. www.phys.unsw.edu.au/music

20. Next lecture Sound waves and Perception of sound Read §16.1–16.3