Interference wave have solution need explanation

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SUMMARY

The discussion focuses on calculating the smallest radius (r) of a half-circle tube that results in an intensity minimum due to destructive interference of sound waves with a wavelength of 46.4 cm. The speed of sound is given as 343 m/s. The key conclusion is that the path length difference must equal half the wavelength (23.2 cm) to achieve this minimum intensity at the detector. This is a fundamental principle of wave interference, specifically applicable to sound waves in cylindrical geometries.

PREREQUISITES
  • Understanding of wave interference principles
  • Knowledge of sound wave properties, including wavelength and speed
  • Familiarity with basic geometry of circular arcs
  • Ability to apply the concept of path length difference in wave mechanics
NEXT STEPS
  • Study the principles of destructive interference in wave mechanics
  • Learn how to calculate path length differences in circular waveguides
  • Explore the effects of varying tube radii on sound wave interference
  • Investigate applications of wave interference in acoustics and engineering
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, acoustics, and sound engineering. This discussion is also beneficial for educators seeking to explain concepts of interference and sound wave behavior.

Puchinita5
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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?
 
Physics news on Phys.org
HINT: A minimum means that destructive interference has occurred ...
 

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