P17_041.PDF

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Chapter 17 - 17.41
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 . 25cm.
(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 ) = 120cm / s.
(c) The distance between nodes is half a wavelength: d = λ/ 2= π/k = π/ ( π/ 3cm − 1 )=3 . 0cm. 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,
3 cm − 1 (1 . 5cm) sin 40 π s − 1 9
8 s =0 .
u =
−
(40 π rad / s)(0 . 50cm)sin π

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