A Thermometer. Suppose you have a tube of length L containing a gas whose temperature you want to take, but you cannot get inside the tube. One end is closed, and the other end is open but a small speaker producing sound of variable frequency is at that end. You gradually increase the frequency of the speaker until the sound from the tube first becomes very loud. With further increase of the frequency, the loudness decreases but then gets very loud again at still higher frequencies. Call fo the lowest frequency at which the sound is very loud.
(a) Show that the absolute temperature of this gas is given by T = 16ML2fo2/yR, where M is the molar mass of the gas, y is the ratio of its heat capacities, and R is the ideal gas constant.
(b) At what frequency above to will the sounds from the tube next reach a maximum in loudness?
(c) How could you determine the speed of sound in this tube at temperature T?