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The function y(x, t) = (18.0 cm) cos(TX-27mt), with x in meters and t in seconds, describes a wave on a taut string, what is the transverse speed for a point on the string at an instant when that point has the displacement y = +15.0 cm?

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Answer #1

A = 18 cm = 0.18 m

y = 15 cm = 0.15 m

y(x,t) = A cos (kx - wt)

w = 27 pi

v = w * sqrt [A2 - y2]

= 27 pi * sqrt [0.182 - 0.152]

transverse speed = 8.44 m/s

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