A long, horizontal pipe is alternately filled with (a) helium and (b) air, each at the same temperature T=300K. A short sound pulse is emitted at one open end and its reflection from the closed far end is detected after a measured time interval t=3.00×10−3s.
(i) Derive an expression for the length L of the pipe in terms of t, γ, R, T, and the molar mass M of the gas used.
(ii) Using γ=1.66,M=4g mol−1 for helium and γ=1.4,M=29g mol−1 for air, calculate the pipe length in each case.
(iii) Explain briefly why the length obtained with helium differs from that obtained with air, even though the physical length of the pipe is unchanged.