A copper rod is heated from 20∘C to 120∘C. Over this temperature range, its Young’s modulus decreases by 3% while its density decreases by 0.7%.
(i) Starting from the relation between speed of sound, elastic modulus and density, obtain an expression for the fractional change in the speed of sound vΔv in terms of the small fractional changes in modulus EΔE and density ρΔρ.
(ii) Using the expression derived in (i), calculate the percentage change in the speed of sound in the copper rod due to heating.
(iii) If the speed of sound in the rod at 20∘C is 4600m s−1, find its value at 120∘C.