Longitudinal Standing Waves and Harmonic Series in Open

and Closed TubesPhysics of Music, Spring 2015

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

Analogy to Transverse Waves

Pressure waves are sine waves – just like a standing wave on a string instrument!

Kundt’s Tube: Standing waves in wind instruments

P + ½ rV2 = constant

Bernoulli’s Equation for Fluids

Pressure goes up, velocity goes down (and vice-versa) Energy divided random and chaotic

pressure density velocity

Open-open Tube

Always “clamped” at atmospheric pressure

Closed-open Tube

Always “clamped” at atmospheric pressureZero net flow of air molecules

Reflections

Phase Change No Phase Change

The Fipple: Divides Airstream

http://homepages.ius.edu/kforinas/S/12Tubes.html

Harmonic Series

Open-Open Open-Closed

Harmonics: Velocity vs Pressure

Open-open tubes Closed-open tubes

Harmonic Scale

Flute

Clarinet (missing even harmonics)

Kundt’s Tube

Brass InstrumentsHow the valves on a trumpet work? Why does pushing down a valve change the note that sounds?

Condenser Microphone

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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

Z = DP/u

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