In a resonance column experiment, a tuning fork of frequency 400 Hz...

Let $e$ be the end correction, which is the distance above the open end where the pressure node forms.

For the first resonance, the length of the air column is $L_1 = 20.0 \text{ cm}$. The relation is:

$L_1 + e = \dfrac{\lambda}{4}$

For the second resonance, the length of the air column is $L_2 = 62.0 \text{ cm}$. The relation is:

$L_2 + e = \dfrac{3\lambda}{4}$

Multiplying the first equation by $3$ and equating it to the second equation, we get:

$3(L_1 + e) = L_2 + e$

$3L_1 + 3e = L_2 + e$

$2e = L_2 - 3L_1$

$e = \dfrac{L_2 - 3L_1}{2}$

Substituting the given values:

$e = \dfrac{62.0 - 3(20.0)}{2}$

$e = \dfrac{62.0 - 60.0}{2}$

$e = \dfrac{2.0}{2} = 1.0 \text{ cm}$