Q 11-14-033JEE MainJEE Main 2026 (28 Jan, Shift 2)Easy
The speed of a longitudinal wave in a metallic bar is 400 m/s. If the density and Young's modulus of the bar material are increased by 0.5% and 1%, respectively then the speed of the wave is changed approximately to ______ m/s.
Answer: (C) 401
$$v = \sqrt{\frac{Y}{\rho}} \Rightarrow \frac{\Delta v}{v} = \frac12\frac{\Delta Y}{Y} - \frac12\frac{\Delta\rho}{\rho} = \frac12(1\%) - \frac12(0.5\%) = 0.25\%$$
$$v' = 400\times1.0025 = 401\ \text{m/s}$$
Solution by Sreeraj P, M.Sc Physics