In a resonance column experiment, a tuning fork of frequency 400 Hz is utilized. The first resonance is noticed when the length of the air column is 20.0 cm , while the second resonance occurs when the air column length is 62.0 cm . How much distance above the open end does the pressure node form?

Step-by-step solution

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 L₁ = 20.0 cm . The relation is: L₁ + e = 4 For the second resonance, the length of the air column is L₂ = 62.0 cm . The relation is: L₂ + e = 3 4 Multiplying the first equation by 3 and equating it to the second equation, we get: 3(L₁ + e) = L₂ + e 3L₁ + 3e = L₂ + e 2e = L₂ - 3L₁ e = L₂ - 3L₁ 2 Substituting the given values: e = 62.0 - 3(20.0) 2 e = 62.0 - 60.