The displacement of a semi-infinite elastic string is determined from a^{2} \frac{\partial^{2} u}{\partial x^{2}}=\frac{\partial^{2} u}{\partial t^{2}}, \quad x>0, t>0 u(0, t)=f(t), \quad \lim _{x \rightarrow \infty} u(x, t)=0, t>0 u(x,

0)=0,\left.\quad \frac{\partial u}{\partial t}\right|_{t=0}=0, x>0