We already know that $v_s = f\lambda$ where $v_s$ is the velocity of sound wave. Now as per my teacher, if we use a resonance tube to calculate the speed of sound, we first measure the length say $l_1$ for the fundamental frequency and then we measure the length say $l_2$ for the 3rd harmonic frequency and since the resonance tube acts like a closed end organ pipe, $l_1 =\frac{\lambda}{4}$ and $l_2 = \frac{3\lambda}{4}$.
And then he used the equation :
$l_2-l_1 = \frac{\lambda}{2}$
$\implies l_2 - l_1 = \frac{v_s}{2f}$ and since in the experiment we know the frequency because of the tuning fork we used we can calculate velocity of sound by $2f(l_2-l_1)$. Now my question is that why not simply calculate velocity of sound using $v_s = f\cdot 4l_1$ or $v_s = f\cdot \frac{4l_2}{3}$ ? My teacher said that its because $l_1$ is actually effective length and so is $l_2$ and when we take their difference the end correction gets cancelled. But aren't we supposed to include end correction in the calculation ?