Three pieces of string, each of length  $L,$   are joined together end to end, to make a combined string of length   $3L.$The first piece of string has mass per unit length ${\mu }_2=4{\mu }_1,$  , the second piece has mass per unit length ${\mu }_1$  and the third piece has mass per unit length ${\mu }_3=\frac{{\mu }_1}{4}.$   If the combined string is under tension F, how much time does it take a transverse wave to travel the entire length  $3L$ ? Give your answer in terms of  $L,F,$  and  ${\mu }_1$  . If your answer is  $\left(\frac{\alpha L}{2}\right)\sqrt{\frac{{\mu }_1}{F}}$   fill value of  $\alpha .$