A well with vertical sides and water at the bottom resonates at7.00 Hz and at no

Question

A well with vertical sides and water at the bottom resonates at7.00 Hz and at now lower frequency. (The air-filled portion of thewell acts as a tube with one closed end and one open end). The airin the well has a density of 1.10kg/m^3 and a bulk modulus of 1.33x 10^5 Pa. How far down in the well is the water surface?
Okay so i've tried approaching this question for a long whilebut got stuck.
so from the one closed end and one open end we know that therewill be a node at the closed end and an antinode at the openend

that gives us a formula to use involving frequency being equalto (2n-1)/4L x v
thats according to what i have in notes, but im quite confusedwith what to do for this quesiton, sorry if i am all over theplace..
So i'm assuming we're trying to find the length of the well? ithink in order to find that we need to find the wavelengthfirst?
Okay so i've tried approaching this question for a long whilebut got stuck.
so from the one closed end and one open end we know that therewill be a node at the closed end and an antinode at the openend

that gives us a formula to use involving frequency being equalto (2n-1)/4L x v
thats according to what i have in notes, but im quite confusedwith what to do for this quesiton, sorry if i am all over theplace..
So i'm assuming we're trying to find the length of the well? ithink in order to find that we need to find the wavelengthfirst?
that gives us a formula to use involving frequency being equalto (2n-1)/4L x v
thats according to what i have in notes, but im quite confusedwith what to do for this quesiton, sorry if i am all over theplace..
So i'm assuming we're trying to find the length of the well? ithink in order to find that we need to find the wavelengthfirst?

Explanation / Answer

All of what you have is right. However, what you need isthe velocity. You can find this by using theformula     v=(B/) where B is thebulk modulus and is the density of the air. Once youget that, you can plug into the formula v=f where isthe wavelength and f is the frequency. then set thewavelength equal to the formula you derived and solve for thelength.   Hope that helped. ask if you have anymore questions.

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