A student uses a tuning fork of known frequency \(f\) to excite standing sound waves in a cylindrical tube open at the top and closed at the bottom by water. Due to boundary effects at the open top, a displacement antinode forms at a distance \(\Delta L\) above the top opening of the tube. The student measures an air column length \(L_1\) for the fundamental resonance and a length \(L_2\) for the next higher resonance. Which of the following expressions correctly gives the speed of sound \(v\) in air and the end correction \(\Delta L\)?