Speed of waves

Let the speed of longitudinal wave be ${ v }_{ L }$ and that of transverse wave be $$ . Now, according to Laplace and Newton's formula for speed of wave in wire,

${ v }_{ L }\quad =\quad \sqrt { \frac { Y }{ \rho } }$ where $'Y'$ is the Young's modulus, and $'\rho$ is the density of the wire.

Also, speed of transverse wave in a wire is

${ v }_{ T }\quad =\quad \sqrt { \frac { T }{ \mu } }$ , where $'T'$ is the tension produced in the wire, and $'\mu'$ is the mass per unit length.

Now, according to question,

$\quad \quad \quad { v }_{ L }=10 \times { v }_{ T }\\ \Rightarrow \sqrt { \frac { Y }{ \rho } } =10\sqrt { \frac { T }{ \mu } }\\ \Rightarrow \frac { Y }{ \rho } =100\frac { T }{ \mu } \\ \Rightarrow \frac { \frac { Stress }{ Strain } }{ \frac { Mass }{ Volume } } =100\frac { Stress \times Area }{ \frac { Mass }{ length } } \\$

where ${ Stress \times Area }$ represents tension in the wire.

Now, putting $Volume = Area \times Length$ and cancelling like terms we get:

$Strain = 0.01$

Cheers!!