A sample of dry air is maintained at a constant pressure while its temperature is slowly varied in the laboratory.
a. (i) Write the general expression that relates the speed of sound v in a gas to its pressure p, density ρ and ratio of specific heats γ.
b. (ii) Using the ideal-gas relation between p,ρ and the absolute temperature T, show algebraically that, at constant pressure, the speed of sound in the gas is proportional to T.
c. (iii) Explain physically why the speed of sound increases with rise in temperature even though the gas density also changes.