Standing WAVES

Kaitlin McNeil
Mind Map by Kaitlin McNeil, updated more than 1 year ago More Less
Kaitlin McNeil
Created by Kaitlin McNeil about 4 years ago
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A note on standing waves
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Standing WAVES
1 modes
1.1 normal mode
1.1.1 A motion in which all particles of the string move sinusiodally w the same frequency
1.1.1.1 Fundamental frequency n=1, L=lambda/2
1.1.2 n= # of anti nodes
2 modes
2.1 linear resonator
2.1.1 n=#of antinodes
2.2 musical instruments may play the same fundamental frequency but have different undertones.
3 mathematical annalysis
3.1 1D
3.1.1 y(x,t) f(x) cos (wt+phi)
3.1.1.1 we can choose to say that the max displacement occurs at t=0 then phi=0
3.1.1.1.1 the 1D wave eqn can then be subbed in
3.1.1.1.1.1 thus f(x)=Asin(w/v x)+Bcos (w/v x)
3.1.1.1.1.1.1 Apply boundary conditions
3.1.1.1.1.1.2 A cannot =0
3.2 any function can be approximated by sim
4 General soln for taught string y(x,t)=Asin (npix/L)cos (wt)
5 Energy in a wave
5.1 K=u
5.1.1 small angle apptoximation sin theta = theta
5.2 ∆S>∆x
6 super position of normal modes
6.1 when you activate one wave you are activating a multitude of standing waves, which is why we consider the summation see eqn 17
6.1.1 timber results from different wave shapes
6.1.1.1 by adding more modes we achieve better agreement esp w respect to the sharp corner
6.1.2 the first harmonic is most important
6.1.3 gob only interested in sin expansion
7 Energy of Vibration of a string
7.1 0
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