Standing waves and Normal modes

Standing wavesandNormal modesLecture 7Pre-reading: 16.1Standing WavesFormed through reflection + superposition of waves moving in opposite directionsContains 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: fundamentalHigher freq. normal modes: harmonics/overtones

15.8Longitudinal WavesDisplacement is in direction of wave motionNeed to distinguish particles from pressure16.1

Three ways to describe sound wavesPressure is 900 out of phase with displacement!Sound as Pressure WaveLongitudinal Standing WavesWaves reflect at open or closed end Need to distinguish displacement of particles from pressureNode: no displacementAnti-node: Time-averaged location where max displacement is reachedDispl. node = Pressure anti-nodeDispl. anti-node = Pressure node

Open pipesClosed pipesfn = n/(2L), n = 1, 2, 3, fn = n/(4L), n = 1, 3, 5, 16.4Interlude:Musical instrumentsMusical instruments use the properties of normal modes to make music.

Instrument design allow players to produce note of desired frequency

One oscillator

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fnotef165 HzC2f2130 HzC3f3195 HzG3f4260 HzC4f5325 HzE4f6390 HzG4f7455 HzB4f8520 HzC5...etcear interprets ratio of frequencies as intervals,

e.g. f2: f1 = 2 octavef2: f1 = 1.5 fifthetc.One oscillator per note

http://en.wikipedia.org/wiki/Sydney_Opera_House_Grand_Organ

pressing fingers on fingerboard changes length of string frequency f

Changing the length of the oscillator

fingerholes change length of pipespeaker hole (thumb hole) forces 2nd harmonicrecorder from http://www.arthursclipart.com/music/musiccol/Recorder.gifwave form from Measured TonesTrombone tube is about 275cm long.

http://en.wikipedia.org/wiki/Trombone

To get other notes:add slide

add valvesAll designed to increase length of pipe increase wavelength Clarinet

Clarinet

www.phys.unsw.edu.au/music/clarinetwww.phys.unsw.edu.au/musicNext lectureSound wavesandPerception of sound

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