Serway & Jewett — Superposition and Standing Waves: Problem 23

An air column in a glass tube is open at one end and closed at the other by a movable piston. The air in the tube is warmed above room temperature, and a 384-Hz tuning fork is held at the open end. Resonance is heard when the piston is at a distance \(d_1 = 22.8 \text{ cm}\) from the open end and again when it is at a distance \(d_2 = 68.3 \text{ cm}\) from the open end. (a) What speed of sound is implied by these data? (b) How far from the open end will the piston be when the next resonance is heard?