The Week Ahead… Mon: Waves on stringed instruments (lab 4) Tues: Oscillations in wind instruments (lab 5) Wed: No class; work on your labs and hw assignment.

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Presentation transcript:

The Week Ahead… Mon: Waves on stringed instruments (lab 4) Tues: Oscillations in wind instruments (lab 5) Wed: No class; work on your labs and hw assignment Thur: Harmonic Series Analysis (lab 6) Fri: Fun demos! DUE DATES: Labs 4 and 5 due Friday at beginning of class. HW 1 due Friday, 5pm

Standing Waves: Modes of Oscillation and Harmonic Series Phys/Mus 102 Spring 2014

Resonance Every oscillating system has a natural frequency. Force on object occurs exactly in phase with the displacement, leading to a “build up” of maximal displacement.

Key terms Resonance Reflection, fixed end, free end Superposition Standing wave Node/anti-node Harmonic series Mersenne’s Law Chladni pattern

Reflection Hard Boundary/Fixed End  Phase change! Soft boundary/Free End  No phase change

Standing Waves Result from superposition of incident waves and reflected waves Only certain wavelengths/frequencies are allowed!

Harmonic Series f 1, 1 st harmonic (fundamental) f 2, 2 nd harmonic f 3, 3 rd harmonic

A few more in the series… Question: What will you hear if you touch your finger to the middle of the string?

The overtone series notes

Mersenne’s Law f 1 = fundamental frequency L = length of string T = tension in string  = mass per unit length of string

Mersenne’s Law Generalized Nth harmonic occurs at frequency: N = 1 = first harmonic N = 2 = second harmonic N = 3 = third harmonic …

What happens with more complex objects: Pianos, Drums, Guitars, Violins, etc? Chladni Patterns

Modes on Guitar String

More Chladni Patterns (Guitar!) Instruments with complex structures have harmonic series/ resonance frequencies too!

Guitar Bracing

Chladni Patterns (Drums!) Animations courtesy of Dan Russel, Kettering University.

Piano soundboard modes

Chladni Patterns (Violin!)

Image/Animation Sources _to_buying_your_first_guitar.html _to_buying_your_first_guitar.html Berg and Stork, Physics of Sound, 3 rd ed