4049115
Descrição
Mapa Mental por Kaitlin McNeil, atualizado more than 1 year ago
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Criado por Kaitlin McNeil
aproximadamente 9 anos atrás
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Standing WAVES
- modes
- normal mode
- A motion in which all particles of the string move sinusiodally w the same frequency
- Fundamental frequency n=1, L=lambda/2
- Fundamental frequency n=1, L=lambda/2
- n= # of anti nodes
- A motion in which all particles of the string move sinusiodally w the same frequency
- normal mode
- modes
- linear resonator
- n=#of antinodes
- n=#of antinodes
- musical instruments may play the same fundamental frequency but have different undertones.
- linear resonator
- mathematical annalysis
- 1D
- 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
- Apply boundary conditions
- thus f(x)=Asin(w/v x)+Bcos (w/v x)
- the 1D wave eqn can then be subbed in
- we can choose to say that the max displacement occurs at t=0 then phi=0
- y(x,t) f(x) cos (wt+phi)
- any function can be approximated by sim
- 1D
- General soln for taught string y(x,t)=Asin (npix/L)cos (wt)
- Energy in a wave
- K=u
- small angle apptoximation sin theta = theta
- small angle apptoximation sin theta = theta
- ∆S>∆x
- K=u
- super position of normal modes
- when you activate one wave you are activating a multitude of standing waves, which is why we consider the summation see eqn 17
- timber results from different wave shapes
- by adding more modes we achieve better agreement esp w respect to the sharp corner
- by adding more modes we achieve better agreement esp w respect to the sharp corner
- the first harmonic is most important
- gob only interested in sin expansion
- timber results from different wave shapes
- when you activate one wave you are activating a multitude of standing waves, which is why we consider the summation see eqn 17
- Energy of Vibration of a string
- 0
- 0
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