1 / 20

Standing waves and Normal modes

Lecture 7. Standing waves and Normal modes. Pre-reading : §16.1. Standing Waves. Formed through reflection + superposition of waves moving in opposite directions Contains ‘nodes’ (no displacement) and ‘anti-nodes’ (maximum displacement)

idalia
Download Presentation

Standing waves and Normal modes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

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

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

  14. Trombone tube is about 275cm long.

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

  16. Clarinet

  17. Clarinet

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

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

More Related