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

AI Thread Summary
To calculate the depth of the well based on the standing sound waves at frequencies of 48, 80, and 112 Hz, it's essential to recognize that these frequencies correspond to consecutive harmonics in a closed tube. The speed of sound is given as 343 m/s, which can be used to determine the wavelengths associated with each frequency using the formula wavelength = speed of sound / frequency. The depth of the well can then be calculated by relating the wavelengths to the harmonics, considering that the fundamental frequency and its harmonics will dictate the well's depth. It is crucial to analyze the relationship between the frequencies and the harmonics to find the correct depth. Understanding these principles will guide the solution to the problem effectively.
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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