Standing waves and Normal modes

1. Lecture 7 Standing wavesandNormal modes 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. Sound as Pressure Wave Three ways to describe sound waves Pressure is 900 out of phase with displacement!

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-nodeDispl. anti-node = Pressure node

6. Open pipes Closed pipes fn = nυ/(2L), n = 1, 2, 3, … fn = nυ/(4L), 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. ear interprets ratio of frequencies as intervals, e.g. f2: f1 = 2 ⇒ octave f2: f1 = 1.5 ⇒ fifth etc.

11. One oscillator per note

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

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

18. Clarinet

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

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