lecturenotes-April12

lecturenotes-April12 - 7 As 7 Bs 11 Cs 6 Ds 19% As 19% Bs...

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Unformatted text preview: 7 As 7 Bs 11 Cs 6 Ds 19% As 19% Bs 30% Cs 16% Ds k = 2 = 2 T phase : kx t kx + t kx t Wave traveling in + x direction Wave traveling in - x direction Transverse Traveling Wave y ( x ,0) = y max sin kx ( ) k = 2 Spatially Periodic ( repeats ) : k = 2 Wave number Wavelength Transverse: Displacement of particle is perpendicular to the direction of wave propagation Longitudinal: Displacement (vibration) of particles is along same direction as motion of wave Traveling Waves- they travel from one point to another Standing Waves- they look like theyre standing still v wave = dx dt = k = T = f Wave Speed 1610:Principle of Superposi4on of Waves Special Case, same k and but phase difference y 1 ( x , t ) = y m sin( kx t ) y 2 ( x , t ) = y m sin( kx t + ) sin + sin = 2sin + ( ) 2 cos ( ) 2 y '( x , t ) = 2 y m cos 2 sin( kx t + 2 ) 2 y m cos 2 is the amplitude of the wave Special Case, same k but s different and no phase difference y 1 ( x , t ) = y m sin( kx t ) y 2 ( x , t ) = y m sin( kx + t ) sin + sin = 2sin + ( ) 2 cos ( ) 2 y '( x , t ) = 2 y m cos t [ ] sin( kx ) 1610:Principle of Superposi4on of Waves Special Case, same k and but phase difference y 1 ( x , t ) = y m sin( kx t ) y 2 ( x , t ) = y m sin( kx t + ) sin + sin = 2sin + ( ) 2 cos ( ) 2 y '( x , t ) = 2 y m cos 2 sin( kx t + 2 ) 2 y m cos 2 is the amplitude of the wave Special Case, same k but s different and no phase difference y 1 ( x , t ) = y m sin( kx t ) y 2 ( x , t ) = y m sin( kx + t ) sin + sin = 2sin + ( ) 2 cos ( ) 2 y '( x , t ) = 2 y m cos t [ ] sin( kx ) Standing Wave n = 2 L n : n=0, 1, 2, 3 -- f n = v n = 1 n = n 2 L T n = 1 f n = n v = 2 L nv = 2 L n 1 = 2 L T 1 = 2 L v 2 = L = 1 2 T 2 = L v = T 1 2 3 = 2 L 3 = 1 3 T 3 = 2 L 3 v = T 1 3 Problem 1633: Interference of Waves Two sinusoidal waves with the same amplitude y m =9.00 mm and the same wavelength travel together along a string that is stretched along the x axis. Their resultant wave is shown twice in the figure, as the valley A travels in the negative direction by a distance d=56.0 cm in t=8.0 ms....
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lecturenotes-April12 - 7 As 7 Bs 11 Cs 6 Ds 19% As 19% Bs...

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