Interference wave have solution need explanation

[Puchinita5]

Homework Statement

In Fig. 17-35, sound with a 46.4 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 (cm) that results in an intensity minimum at the detector? (Take the speed of sound to be 343 m/s.)

Homework Equations

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c17/pict_17_34.gif

The Attempt at a Solution

i have the solution...what i don't understand is WHY the path length difference equals 23.2? don't see how or why it's half the wavelength?

 

[Hootenanny]

HINT: A minimum means that destructive interference has occurred ...