A well with vertical sides and water at the bottom resonates at 7Hz and at no other lower frequency. The air in the well has density `1.10kgm^(-3)` and bulk modulus of water is `1.33xx10^(5)N//m^(2)`. How deep is the well ?

Explanation

To find the depth of the well that resonates at a frequency of 7 Hz, we can use the relationship between the fundamental frequency of a column of air and its length. The fundamental frequency for a closed pipe (like our well) is given by the formula:

\[ f = \frac{1}{4L} \sqrt{\frac{B}{\rho}} \]

where:
- \( f \) is the frequency (7 Hz),
- \( L \) is the length of the air column (depth of the well),
- \( B \) is the bulk modulus of water (given as \( 1.33 \times 10^5 \, \text{N/m}^2 \)),
...