Interference wave have solution need explanation

AI Thread Summary
The discussion centers on a sound wave interference problem involving a tube with a straight portion and a half-circle. The key question is determining the smallest radius that results in an intensity minimum at the detector, given a wavelength of 46.4 cm and a sound speed of 343 m/s. The participant is confused about why the path length difference is half the wavelength, which is crucial for achieving destructive interference. It is clarified that a minimum in intensity indicates destructive interference, which occurs when the path length difference equals half the wavelength. Understanding this concept is essential for solving the problem effectively.
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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?
 
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HINT: A minimum means that destructive interference has occurred ...
 

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