Dry air in a sealed horizontal tube is initially at 1.0 atm and 300 K. The speed of sound in this state is v0. The air is now compressed isothermally until its density becomes 1.5 times the initial value, after which the temperature is again 300 K.
(a) Derive an expression relating the new speed of sound v to v0 in terms of the change in density.
(b) Calculate the percentage change in the speed of sound due to this compression.
(c) The tube is 3.0 m long. Find the time taken by a short sound pulse to travel from one end of the tube to the other (i) before compression and (ii) after compression. Compare the two times.