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  Kundt’s Tube

Kundt’s Tube: Standing waves in wind instruments

P + ½  V 2 = constant Bernoulli’s Equation for Fluids  Pressure goes up, velocity goes down (and vice- versa)  Energy is divided into random (pressure) and ordered motion (kinetic energy) pressure densityvelocity

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

Harmonic Series Open-Open Open-Closed

Harmonics: Velocity vs Pressure

Harmonic Scale Flute Clarinet (missing even harmonics)

Kundt’s Tube

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

Condenser Microphone

Sources  Univ. of New South Wales Acoustics Research Group:    (Kundt’s Tube) 

Acoustic Impedance Z =  P/u How much pressure it takes to induce a certain amount of air to flow