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


A note on standing waves

Resource summary

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 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) we can choose to say that the max displacement occurs at t=0 then phi=0 the 1D wave eqn can then be subbed in thus f(x)=Asin(w/v x)+Bcos (w/v x) Apply boundary conditions 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 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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