• Tags: resonance-tube, standing-wave, end-correction
• Difficulty: Moderate

A tuning fork of known frequency f is held over a tube whose water level can be adjusted. Resonance occurs when the air column length matches a standing wave condition. First resonance: $l_1$ + e = lambda/4. Second resonance: $l_2$ + e = 3lambda/4. Third: $l_3$ + e = 5lambda/4. Taking the difference: $l_2$ - $l_1$ = lambda/2, so lambda = 2*($l_2$ - $l_1$). Speed: v = flambda = 2f*($l_2$ - $l_1$). End correction: e = $\frac{l_2 - 3*l_1}{2}$ ≈ 0.3d (where d is the tube's inner diameter). By using the difference $l_2$ - $l_1$, the end correction cancels — a key advantage. The antinode forms slightly outside the tube (by distance e). Higher harmonics (third resonance at $l_3$) can verify the result: $l_3$ - $l_2$ should also equal lambda/2. Temperature affects speed: v = 331 + 0.6T(degrees C) m/s at standard conditions.