Question

A sonometer consists of two wires of same material whose radii are in the ratio $2:3$. The tension in thick wire is $4$ times the tension in thin wire. If $V$ is velocity of transverse wave in thin wire, then the velocity of transverse wave in thick wire is

• A. $\frac{3V}{4}$
• B. $\frac{3V}{2}$
• C. $\frac{2V}{3}$
• D. $\frac{4V}{3}$

Answer 1

The correct option is D $\frac{4V}{3}$

Given : $\frac{r_1}{r_2}=\frac{2}{3}$
$\frac{T_1}{T_2}=\frac{1}{4}$
$v=\sqrt{\frac{T}{m/l}}$
$=\sqrt{\frac{T}{\rho \pi r^2}}$
so, $\frac{v_1}{v_2}=\frac{\sqrt{\frac{T_1}{\rho \pi r_1{}^2}}}{\sqrt{\frac{T_2}{\rho \pi r_2{}^2}}}$
$=\sqrt{\frac{T_1}{T_2}\times \frac{r_2{}^2}{r_1{}^2}}$
$=\sqrt{\frac{1}{4}\times (\frac{3}{2}{)}^2}$
$=\frac{3}{4}$
so, $v_2=v_1\frac{4}{3}=\frac{4}{3}V$