• 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 = (l_2 - 3l_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 + 0.6*T(degrees C) m/s at standard conditions.