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Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes. Physics of Music, Spring 2014. Key terms. Bernoulli’s Equation Pressure vs. velocity Compression vs. rarefaction Open tube Closed tube Boundary condition—phase change Node vs. anti-node Even and Odd harmonics

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longitudinal standing waves and harmonic series in open and closed tubes

Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes

Physics of Music, Spring 2014

key terms
Key terms
  • Bernoulli’s Equation
  • Pressure vs. velocity
  • Compression vs. rarefaction
  • Open tube
  • Closed tube
  • Boundary condition—phase change
  • Node vs. anti-node
  • Even and Odd harmonics
  • Kundt’s Tube
bernoulli s equation for fluids
Bernoulli’s Equation for Fluids

P + ½rV2 = constant

density

velocity

pressure

  • Pressure goes up, velocity goes down (and vice-versa)
  • Energy is divided into random (pressure) and ordered motion (kinetic energy)
open open tube
Open-open Tube

Always “clamped” at atmospheric pressure

slide6

Closed-open Tube

Zero net flow of air molecules

Always “clamped” at atmospheric pressure

reflections
Reflections

No Phase Change

Phase Change

harmonic series
Harmonic Series

Open-Open

Open-Closed

harmonic scale
Harmonic Scale

Flute

Clarinet (missing even harmonics)

brass instruments
Brass Instruments

How the valves on a trumpet work?

Why does pushing down a valve change the note that sounds?

sources
Sources
  • Univ. of New South Wales Acoustics Research Group:
  • http://www.phys.unsw.edu.au/jw/flutes.v.clarinets.html
  • http://www.phys.unsw.edu.au/jw/pipes.html
  • (Kundt’s Tube) http://www.youtube.com/watch?v=qUiB_zd9M0k
  • http://www.mediacollege.com/audio/microphones/condenser.html
acoustic impedance
Acoustic Impedance

How much pressure it takes to induce a certain amount of air to flow

Z = DP/u