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2.1 Introduction to Waves

2.1 Introduction to Waves - 2.1Waves ScienceofMusic 2007...

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2.1 Waves Science of Music 2007

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A Brief Return to Last Time We discussed oscillations of springs and  pendulums.  We defined frequency f and period T=(1/f). We also reviewed Newton’s Laws: An object in motion will tend to move at the same  velocity unless acted upon by an external force. Constant velocity or static conditions are both referred  to as equilibrium . F=ma Action = Reaction
Last time: Concept … Tension

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Which force (a “vector”) pulls UP more: F F
The Musical String Force = F x L initial T T T The Bigger the angle the more T points UP! The distance “x” is the same sort of thing as the x in F=-kx. ANGLE

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The Guitar Strings
Consider Two Situations For the same “x” the restoring force is double because the angle is  double. The “mass” is about half because we only have half of the string vibrating.

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So… For the same “x” the restoring force is double because the angle is  double. The “mass” is about half because we only have half of the string vibrating. m k f kx F π 2 1 = - = k doubles m -> m/2 f doubles!
It has been shown that … k" " constant spring a like Looks area sectional - cress the is A material a for constant a is E with pull you force the is F = initial stretch initial L EA L L EA F The “stretch” produces the restoring force.

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Guitar Pressing the fret that is in the middle of the  string doubles the frequency~ Walla … the octave In general … the frequency is proportional  to the length of the string.
Interlude…..

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2.1 Introduction to Waves - 2.1Waves ScienceofMusic 2007...

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