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 .

Step-by-step solution

The speed of a longitudinal wave in a solid is given by v = Y where Y is Young's modulus and is density. Initial condition: v₀ = Y = 400 m/s After changes: ' = 1.005 (0.5% increase) and Y' = 1.01Y (1% increase) New speed: v' = Y' ' = 1.01Y 1.005 = 1.01 1.005 Y v' v₀ = 1.01 1.005 = 1.00498... 1.00249 v' = 400 1.00249 401 m/s