P17_047 - 47. (a) The angular frequency is = 8.0/2 = 4.0...

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47. (a) The angular frequency is ω =8 . 0 π/ 2=4 . 0 π rad / s, so the frequency is f = ω/ 2 π =(4 . 0 π rad / s) / 2 π = 2 . 0Hz. (b) The angular wave number is k =2 . 0 π/ 2=1 . 0 π m 1 , so the wavelength is λ =2 π/k =2 π/ (1 . 0 π m 1 )= 2 . 0m. (c) The wave speed is v = λf =(2 . 0 m)(2 . 0Hz)=4 . 0m / s . (d) We need to add two cosine functions. First convert them to sine functions using cos α = sin( α + π/ 2), then apply Eq. 42. The steps are as follows: cos α +cos β = sin ³ α + π 2 ´ + sin ³ β + π 2 ´ = 2 sin µ α + β + π 2 cos µ α β 2 =2 c o s µ α + β 2 cos µ α β 2 Letting α = kx and β = ωt , we ±nd y m cos( kx + ωt )+ y m cos( kx
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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