Question

A correct experiment is performed to measure the speed of sound in air using a resonance column tube of diameter 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound is given as 336 m/s. The zero of the metre scale coincides with the top end of the resonance column tube. The reading of the water level in the column tube, when the first resonance occurs is :

• A. 16.6 cm
• B. 18.4 cm
• C. 14.8 cm
• D. 13 cm

Hint:

Always include the end correction $e = 0.3d$ for resonance tube experiments. The antinode actually forms slightly above the open end of the tube.

Answer 1

The Correct Option is C

Step 1: Calculate wavelength $\lambda = \frac{v}{f} = \frac{336}{504} = \frac{2}{3}$ m $\approx 66.67$ cm.
Step 2: For the first resonance in a closed tube, the effective length is $L_{eff} = \frac{\lambda}{4} = \frac{66.67}{4} = 16.67$ cm.
Step 3: Effective length includes end correction: $L_{eff} = l + e$, where $e = 0.3 \times \text{diameter}$.
Step 4: $e = 0.3 \times 6 = 1.8$ cm.
Step 5: Actual reading $l = L_{eff} - e = 16.67 - 1.8 = 14.87$ cm.