The function y(x,t) = (15cm )cos(pi x -15t pi), with x in meters and t in seconds, describes a wave on taut string. What is the transverse speed for a point on the string at an instant when that point has the displacement y=+12cm?
at that place and time:
12/15 = 4/5 = cos theta
where theta = pi x - 15 pi t
theta = 36.87 degrees = .644 radians
also when theta = 2 pi - .644 of course but same speed then I think
dy/dt = v = 15 (-15 pi)(-sin theta)
if cos theta = 4/5 then sin theta = 3/5
so
dy/dt =
= 225 pi 3/5
= 135 pi cm/s