Standing WAVES

Standing WAVES

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

Resource summary

	Created by Kaitlin McNeil over 8 years ago