Mixtures, cooling and resonance in code

You will write four functions for the experiments on heat and sound. They follow the lesson.

The idea. In the method of mixtures, the heat lost by the hot block equals the heat gained by the liquid and the calorimeter. In Newton's law of cooling, $k = \dfrac{1}{t}\ln\dfrac{\theta_0 - \theta_s}{\theta - \theta_s}$. For a resonance tube, $v = 2f(L_2 - L_1)$ and $e = \dfrac{L_2 - 3L_1}{2}$.

Your tasks.

1. In liquid_specific_heat, return $c_l$ from the heat balance. The inputs are the mass, the specific heat and the temperature of the block, and the final temperature. The others are the mass of the liquid, the heat capacity of the calorimeter and the starting temperature of the liquid.
2. In cooling_constant, return $k$ from the excess of temperature at the start and after a time.
3. In sound_speed, return $v$ in m/s from the frequency in Hz and the two lengths in m.
4. In end_correction, return $e$ from the two lengths.