PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
Air in a closed laboratory is initially at 27∘C. Its speed of sound is measured to be 346ms−1. The same mass of air is then slowly warmed while its composition and pressure are kept unchanged.
(i) Derive an expression for the ratio v1v2 of the speeds of sound at two absolute temperatures T2 and T1 for the same gas kept at the same pressure.
(ii) Hence prove that the percentage change in the speed of sound in a gas equals one-half of the percentage change in its absolute temperature.
(iii) Using the above result, calculate the speed of sound in the laboratory when the temperature reaches 127∘C. Express your answer correct to three significant figures.