51. (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= 40πrad/s and an angular wave number of k= π/3 cm–1. The wave speed isv= /k= (40πrad/s)/(π/3 cm–1) = 1.2×102cm/s. (c) The distance between nodes is half a wavelength: d= λ/2 =
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