The red curve is the initial state at time zero, at which the string is "let free" in a predefined shape with all u ˙ ˙ i = 0 . The blue curve is the state at time L c ⋅ ⋅ 0.25 , i.e. after a time that corresponds to the time a wave that is moving with the nominal wave velocity c = √ f / ρ would need for one fourth of the length of the string.