Question

Two stings A and B of same material are stretched by same tension. The radius of the string A is double the radius of string B. Transverse wave travels on string A with speed '$V_A$' and on string B with speed '$V_B$'. The ratio $\frac{V_A}{V_B}$ is

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

Answer 1

The correct option is B $\frac{1}{2}$

The velocity of the transverse waves on string is given as

$v=\sqrt{\frac{T}{\mu }}$ ..............(1)

where, T is the tension in the string and $\mu$ is the mass per length.

$\therefore \mu =\frac{\pi r^2\rho l}{l}$

$\therefore \mu =\pi r^2\rho$

$\therefore v=\sqrt{\frac{T}{\pi r^2\rho }}$ ..............from (1)

$\therefore v\propto \frac{1}{r}$

where,

r is the radius of string

$\rho$ is the material density for string

Now as per the given problem both strings are of same materials and same tension tension

Therefore,

$\frac{v_A}{v_B}=\frac{r_B}{r_A}$

$\frac{v_A}{v_B}=\frac{r_B}{2r_B}$

$\frac{v_A}{v_B}=\frac{1}{2}$