Question

If the speed of longitudinal wave equals $10$ times the speed of the transverse waves in a stretched wire of material which has modulus of elasticity E, then the stress in the wire is

• A. $100E$
• B. $\frac{E}{100}$
• C. $\frac{E}{10}$
• D. $10E$

Answer 1

The correct option is B $\frac{E}{100}$

$v_l=\sqrt{\frac{Y}{\rho }}$ and $v_t=\sqrt{\frac{Y\frac{\Delta l}{l}}{\rho }}=v_l\sqrt{\frac{\Delta l}{l}}$

$\Rightarrow \sqrt{\frac{l}{\Delta l}}=\frac{v_l}{v_t}=10$

$\therefore \frac{\Delta l}{l}=\frac{1}{100}$

Stress$=Y\frac{\Delta l}{l}=E\frac{\Delta l}{l}=\frac{E}{100}$