Halliday, Resnick & Walker — Waves–II: Problem 22

In Fig. 17.14, sound with a 40.0 cm wavelength travels rightward from a source and through a tube that consists of a straight portion and a half-circle. Part of the sound wave travels through the half-circle and then rejoins the rest of the wave, which goes directly through the straight portion. This rejoining results in interference. What is the smallest radius \( r \) that results in an intensity minimum at the detector?