Find Min Radius for Sound Wave in Tube

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SUMMARY

The discussion centers on calculating the minimum radius required for a sound wave with a wavelength of 40.0 cm to achieve destructive interference at the detector end of a tube. The key equation involved is the wave speed formula, v = λf, where λ represents the wavelength. The challenge arises from the ambiguity regarding whether the tube is closed or open, which affects the wavelength behavior in the tube. The critical factor is determining the minimum path length difference necessary for destructive interference to occur in the circular segment of the tube.

PREREQUISITES
  • Understanding of wave properties, specifically wavelength and frequency.
  • Familiarity with the concept of destructive interference in wave physics.
  • Knowledge of sound wave behavior in closed and open tubes.
  • Basic mathematical skills for calculating lengths and differences.
NEXT STEPS
  • Study the principles of wave interference, focusing on destructive interference conditions.
  • Learn about the behavior of sound waves in closed and open tubes, including harmonic series.
  • Investigate the relationship between wavelength, frequency, and wave speed in different mediums.
  • Explore practical applications of sound wave behavior in acoustics and engineering design.
USEFUL FOR

Students in physics, particularly those studying wave mechanics, acoustics, and sound engineering, will benefit from this discussion.

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Homework Statement


"A sound wave of 40.0 cm wavelength enters the tube shown below at the source end. What must be the smallest radius r such that a minimum will be heard at the detector end?" (figure attached)

Homework Equations


v =[tex]\lambda[/tex][tex]f[/tex]

The Attempt at a Solution


I don't have any idea how to do this problem. My first idea was to use the formula for the wavelength of a closed or open tube, but whether the tube is closed or open isn't given so I'm guessing that's not right. Also, I don't see how the radius of the half circle has anything to do with the tube through which the sound is traveling.

Thanks in advance
 

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The sound travels along both the straight tube and the circular one. The sound wave enters in both tubes with the same phase, but the lengths the waves travel along the different segments will be different. What is the minimum difference between the lengths traveled so as destructive interference occur at the other end of the circular tube?

ehild
 

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