In an early method of determining the speed of sound in gases, powder was spread along the bottom of a horizontal, cylindrical glass tube. One end of the tube was closed by a piston that oscillated at a known frequency f. The other end was closed by a movable piston whose position was adjusted until resonance occurred. At resonance, the powder collected in equally spaced piles along the bottom of the tube.

(a) Explain why the powder collects in this way.

(b) Derive a formula that gives the speed of sound in the gas in terms of f and the distance between the piles of powder.

(c) Give suitable values for the frequency f and the distance between the piles of powder.

(d) Give suitable values for the frequency f and the length L of the tube for which the speed of sound could be measured in either air or helium.