Question

In brass, the velocity of longitudinal wave is 100 times the velocity of the transverse wave. If $Y=1\times 10^{11}N/m^2$, then stress in the wire is

• A. $1\times 10^{13}N/m^2$
• B. $1\times 10^{9}N/m^2$
• C. $1\times 10^{11}N/m^2$
• D. $1\times 10^{7}N/m^2$

Answer 1

Answer: (D)

As $v_L=\sqrt{\frac{Y}{\rho }}$ and $v_T=\sqrt{\frac{T}{\mu }}=\sqrt{\frac{T}{\pi r^2\rho }}$
$\therefore \frac{v_L}{v_T}=\sqrt{\frac{Y}{\rho }\times \frac{\pi r^2\rho }{T}}=\sqrt{\frac{Y}{T/\pi r^2}}=\sqrt{\frac{Y}{\text{ stress }}}$
$\therefore$ Stress $=\frac{Y}{{\left(v_L/v_T\right)}^2}=\frac{1\times 10^{11}}{(100{)}^2}=1\times 10^{7}N/m^2$