Fixed Rope and Wave Solution

A rope of length 1 is fixed to a wall at x=0x=0 and shaken at the other end so that

x(1,t)=sinωt.x(1,t) = \sin \omega t.

Which of the following is a possible displacement of the rope as a function of xx and tt consistent with these boundary conditions, assuming the waves of the rope propagate with velocity v=1v=1?

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