A cylindrical pipe of fixed length \(L\) is closed at one end and open at the other. An audio speaker positioned at the open end emits sound at a constant frequency \(f\), which establishes a standing wave corresponding to the third harmonic (first overtone) in the gas inside the pipe at initial absolute temperature \(T_1\). The gas is then uniformly heated to a new absolute temperature \(T_2\) without changing its composition or the pipe length. If the same speaker emitting the same frequency \(f\) now excites the fundamental standing wave mode of the pipe, by what factor must the absolute temperature have changed (\(T_2/T_1\)), and by what factor did the wavelength of the sound wave inside the pipe change (\(\lambda_2/\lambda_1\))?