Question

Two strings A and B, made of same material, are stretched by the same tension. The radius of string A is double of radius of B. A transverse wave travel on A with speed $v_A$ and B with speed $v_B$. The ratio $v_A/v_B$ is

• A. 1/2
• B. 2
• C. 1/4
• D. 4

Answer 1

Answer: (A)

1/2

Given:

The tension developed in the two strings is the same.

The radius of the string $A$ is double the radius of the string $B$.

Wave velocity in a string is given by:
$v=\sqrt{\frac{T}{m}}$

$=\sqrt{\frac{T}{\pi r^2\rho }}$

here $m=\pi r^2\rho$ is the mass per unit length.

So, $v\propto \frac{1}{r}$

$\Rightarrow \frac{v_A}{v_B}=\frac{r_B}{r_A}=\frac{1}{2}$