Question

Two strings $A$ and $B$, made of same material, are stretched by same tension. The radius of string $A$ is double the radius of $B$. A transverse wave travels on $A$ with speed $v_A$ and on $B$ with speed $v_B$. The ratio $\left(\frac{v_A}{v_B}\right)$ is

• A. $\frac{1}{2}$
• B. 2
• C. $\frac{1}{4}$
• D. 4

Answer 1

The correct option is A

$\frac{1}{2}$

Two strings $A$ and $B$, made of same material, are stretched by same tension. The radius of string $A$ is double of the radius of $B$.A transverse wave travels on $A$ with speed $v_A$ and on $B$ with speed $v_B$. The ratio $\left(\frac{v_A}{v_B}\right)$ is

$v$ = $\sqrt{\frac{T}{\mu }}$; as $T$ is constant, $v$ $\propto$ $\frac{1}{\sqrt{\mu }}$

But $\mu$ = $\frac{mass}{length}$ = $\pi r^2\rho$ $\to$ $\mu$ $\propto$ $r^2$

$\Rightarrow$ $v$ $\propto$ $\frac{1}{r}$ $\to$ $\frac{v_A}{v_B}$ = $\frac{r_B}{r_A}$ = $\frac{r}{2r}$ = $\frac{1}{2}$