Q 11-14-145JEE MainJEE Main 2025 (8 Apr, Shift 2)Easy
Two strings with circular cross section and made of the same material are stretched to have the same tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having radius of cross section $R$ is $v_1$, and that in the other string having radius of cross section $R/2$ is $v_2$. Then $\dfrac{v_2}{v_1}$ is:
Answer: (B) $2$
$v = \sqrt{T/\mu}$ with $\mu = \rho\pi r^2$, so $v \propto \dfrac1r$ for the same $T$ and material:
$$\frac{v_2}{v_1} = \frac{R}{R/2} = 2$$
Solution by Sreeraj P, M.Sc Physics