Question

A cylindrical well with vertical sides and water at the bottom resonates at $7$ Hz and at no lower frequency. The air in the well has density $1.1$ kg$/m^3$ and bulk modulus $1.33\times {10}^5$ $N/m^2$. How deep is the well?

Answer 1

The well can be assumed as an organ pipe open at one end. Its fundamental frequency is given by

$n=\frac{v}{4l}$ and $v=\sqrt{B/\rho }$

$\Rightarrow n=\frac{\sqrt{B/\rho }}{4l}$

$\Rightarrow l=\frac{\sqrt{B/\rho }}{4n}=\frac{\sqrt{\frac{1.33\times {10}^5}{1.1}}}{4\times 7}=12.4$ meter.