P17_041 - λ/ 2 = π/k = π/ ( π/ 3 cm − 1 ) = 3 . 0 cm....

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41. (a) The amplitude of each of the traveling waves is half the maximum displacement of the string when the standing wave is present, or 0 . 25 cm. (b) Each traveling wave has an angular frequency of ω =40 π rad / s and an angular wave number of k = π/ 3cm 1 . The wave speed is v = ω/k =(40 π rad / s) / ( π/ 3cm 1 ) = 120 cm / s. (c) The distance between nodes is half a wavelength: d =
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Unformatted text preview: λ/ 2 = π/k = π/ ( π/ 3 cm − 1 ) = 3 . 0 cm. Here 2 π/k was substituted for λ . (d) The string speed is given by u ( x, t ) = ∂y/∂t = − ωy m sin( kx ) sin( ωt ). For the given coordinate and time, u = − (40 π rad / s)(0 . 50 cm) sin h³ π 3 cm − 1 ´ (1 . 5 cm) i sin · ( 40 π s − 1 ) µ 9 8 s ¶± = 0 ....
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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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