The speed of sound from a resonance tube

You will turn the readings of a resonance tube into the speed of sound.

The idea. The first two resonances are half a wavelength apart, so $v = 2f(l_2 - l_1)$. The end correction is $e = \dfrac{l_2 - 3l_1}{2}$, and it is about $0.3d$ for a tube of inside diameter $d$. The first resonance is at $l_1 = \dfrac{v}{4f} - e$. Every length here is in metres.

Your tasks.

1. In speed, return the speed of sound in m/s from $f$, $l_1$ and $l_2$.
2. In end_correction, return $e$ in m from $l_1$ and $l_2$.
3. In first_length, return the first resonance length in m, for a fork $f$, a speed $v$ and a tube of inside diameter $d$.