Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes Physics of Music, Spring 2016.

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Presentation transcript:

Longitudinal Standing Waves and Harmonic Series in Open and Closed Tubes Physics of Music, Spring 2016

Key terms  Bernoulli’s Equation  Pressure vs. velocity  Compression vs. rarefaction  Open vs. Closed Tubes  Node vs. anti-node  Even and Odd harmonics  Kundt’s Tube  Rubens’ Tube

Standing Waves

Analogy: Longitudinal to Transverse Waves Pressure waves are sine waves too!

Longitudinal Standing Waves Animation courtesy of Dan Russsell, Grad Prog Acoustics, Penn State

What causes the oscillation? FippleReed

Fire It Up: Rubens’ Tube  Other good videos:  (Utah’s tube, detailed explanation)  (Portland rubens’ tube, good music)  (Brazil, fun starts about 6’30”, really good music)  (cycles through resonance frequencies, turn your sound off, you don’t go crazy)

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 divided random and chaotic pressure mass density velocity

Time for Reflection Phase ChangeNo Phase Change

Open Tube Pressure nodes: Openings always “clamped” at ~P atm (Velocity antinodes)

Closed Tube Pressure anti-node (Velocity node) Pressure node (Velocity anti-node)

Harmonics: Velocity vs Pressure Open tubes Closed-open tubes

Closed Tubes

Harmonic Scale Flute (open, all harmonics) Clarinet (closed, missing even harmonics)

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

Top Brass

Fire It Up: Rubens’ Tube  Other good videos:  (Utah’s tube, detailed explanation)  (Portland rubens’ tube, good music)  (Brazil, fun starts about 6’30”, really good music)  (cycles through resonance frequencies, turn your sound off, you don’t go crazy)

The Fipple: Divides Airstream

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

Condenser Microphone

Harmonic Series Open-Open Open-Closed

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