Calculating Well Depth: Solving for Standing Sound Waves at 48, 80, and 112 Hz

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SUMMARY

The problem involves calculating the depth of a well based on the frequencies of standing sound waves at 48 Hz, 80 Hz, and 112 Hz, with the speed of sound being 343 m/s. The established frequencies correspond to three consecutive harmonics of a closed tube, where the relationship between wavelength and tube length is crucial. The depth of the well can be determined using the formula for the wavelength of sound waves and the harmonic series. Specifically, the depth can be calculated using the equation: depth = (speed of sound) / (frequency) * (1/2) for the fundamental frequency.

PREREQUISITES
  • Understanding of sound wave properties and harmonics
  • Familiarity with the speed of sound in air
  • Knowledge of wave equations and their applications
  • Basic algebra for solving equations
NEXT STEPS
  • Study the relationship between frequency, wavelength, and harmonic series in closed tubes
  • Learn how to apply the wave equation to calculate depth in similar problems
  • Explore the concept of standing waves and their formation in different mediums
  • Investigate the effects of temperature and pressure on the speed of sound
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Students in physics, acoustics researchers, and engineers working with sound wave applications will benefit from this discussion.

Angie913
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There's this problem I'm having lots of trouble with. It is:
A person hums into the top of a well and finds that the standing waves are established at frequencies of 48, 80, and 112 Hz. The freq. of 48 Hz is not necessarily the fundamental freq. The speed of sound is 343m/s. How deep is the well?
I'm not sure where to start! The only equations we have for height are:
h=.5gt^2
and
h=velocitysound(t2-t1) which doesn't help! I'm not sure what I should use. Any hints are great! Thanks
 
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Okay, if you're lost when considering height, then try looking at the other parts of the problem.
 
Consider the relationship between wavelength and length of a one side closed tube. You may have to assume that the given frequencies corresponds to three consecutive harmonics (n, n+1 and n+2)
 

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