A well with vertical sides and water at the bottom resonates at 6.40 Hz and at no lower frequency

vertical-sides

#1

A well with vertical sides and water at the bottom resonates at 6.40 Hz and at no lower frequency. (The air-filled portion of the well acts as a tube with one closed end and one open end.) The air in the well has a density of 1.10 kg/m3 and a bulk modulus of 1.33 × 105 Pa. How far down in the well is the water surface?

Answer:

For a half closed pipe f = v/4L…so L = v/(4f)
but v = sqrt(B/ρ)
f=6.40
So L = sqrt(B/ρ)/(4f)
= sqrt(1.33x10^5/1.10)/(4*6.40) = 13.5 m.