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A string of length l=1 is initially fixed i the position [itex] u = \sin{\pi x} [/itex] and is released at time t = 0 . Find its subsequent motion

What do they mean by the subsequent motion?? DO they mean the velocity? Do i differnetiate u by time? the answer i know is [itex] u = \sin{\pi x} \cos{ \pi ct} [/itex]

ANd where di they give the c from anyway? The intial u represents the soltuion with the integral part of d'Alembert's soltuion equal to zero, doesn't it?

Please help! Thank you!