If the ratio of the Young's modulii and densities of two rods of different materials are respectivel

Question

If the ratio of the Young's modulii and densities of two rods of different materials are respectively, $3: 2$ and $3: 1$, then the ratio of the velocities of sound in the rods is\

Professor PC Thomas Classes · Answer

(d): Let $Y_{1}$ and $ho_{1}$ be the Young's modulus and density of first rod.\ Let $Y_{2}$ and $ho_{2}$ be the Young's modulus and density of second rod.\ Given that, $\frac{Y_{1}}{Y_{2}}=\frac{3}{2}$ and $\frac{ho_{1}}{ho_{2}}=\frac{3}{1}$\ The velocity of sound in a solid rod is given by, $v=\sqrt{\frac{Y}{ho}}$\ $	herefore \frac{v_{1}}{v_{2}}=\sqrt{\frac{Y_{1}}{Y_{2}} 	imes \frac{ho_{2}}{ho_{1}}}=\sqrt{\frac{3}{2} 	imes \frac{1}{3}}=\frac{1}{\sqrt{2}}$