Standing waves question with harmonics?

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The discussion revolves around determining the depth of a well based on established standing wave frequencies of 42, 70, and 98 Hz, with the speed of sound given as 343 m/s. Participants explore the relationship between these frequencies, noting that 42 Hz is identified as the third harmonic rather than the fundamental frequency. The challenge lies in calculating the well's depth without assuming 42 Hz as the fundamental frequency. The conversation emphasizes using harmonic ratios and the properties of standing waves in an open-closed system to derive the solution. Ultimately, understanding the harmonic relationships is crucial for solving the problem accurately.
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Homework Statement



A person hums into the top of a well and finds that standing waves are established at frequencies of 42, 70 and 98 Hz. The frequency of 42 Hz is not necessarily the fundamental frequency. The speed of sound is 343m/s. How deep is the well?

Homework Equations



just harmonic ratios.

The Attempt at a Solution



i've no clue pls help. since we can't assume that 42Hz is the fundamental.

my first approach was to use the fundamental frequency. find the wavelength and then half of that would be the depth but i don't know how to do it if we can't assume.
 
Last edited:
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Hint: Consider the ratio of one frequency to another, for all pairs.
 
is this system open closed?
 
ok so i figured out that the 42Hz is the third harmonic. now what shall i do?
 
How did you figure out it was the third harmonic?
 

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