The wave function of a sinusoidal wave generated on a string is given by: y$($x$,$t$)=0\mathrm{.}2$ sin $(2$x $+4$t $+$ $).$ At t $=0,$ an element of the string at x $=0$ has a vertical displacement of $0\mathrm{.}1$ m and is moving down. The phase constant is: