A long steel rail is used on a railway track

PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Solids · Mechanical Properties of Solids

Problem

A long steel rail is used on a railway track. The density of steel is 7.8×103 kg m−37.8\times10^{3}\,\text{kg m}^{-3} and its Young’s modulus is 2.0×1011 N m−22.0\times10^{11}\,\text{N m}^{-2}. (i) Derive an expression for the speed of a longitudinal sound wave that travels along the rail in terms of the relevant elastic constant and density of the material. (ii) Using the given data, calculate the speed of sound in the steel rail. (iii) A brass rail has Young’s modulus 1.0×1011 N m−21.0\times10^{11}\,\text{N m}^{-2} and density 8.5×103 kg m−38.5\times10^{3}\,\text{kg m}^{-3}. Find the ratio of the speeds of sound in brass and steel rails.

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