A student is performing the experiment of the resonance column. The diameter of the column tube is 6 cm. The frequency of the tuning fork is 504 Hz. Speed of the sound at the given temperature is 336 m s$$^{-1}$$. The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is:

In a resonance column experiment, the first resonance occurs when the length of the air column plus the end correction equals one-quarter of the wavelength: $$L + e = \frac{\lambda}{4}$$, where $$e$$ is the end correction.

The wavelength of the sound wave is $$\lambda = \frac{v}{f} = \frac{336}{504} = \frac{2}{3}$$ m $$= 66.67$$ cm.

Therefore $$\frac{\lambda}{4} = \frac{66.67}{4} = 16.67$$ cm.

The end correction for a tube of diameter $$d$$ is given by $$e = 0.3d$$. With $$d = 6$$ cm, we get $$e = 0.3 \times 6 = 1.8$$ cm.

The water level reading at first resonance is the length of the air column: $$L = \frac{\lambda}{4} - e = 16.67 - 1.8 = 14.87 \approx 14.8$$ cm.

The correct answer is Option (1): 14.8 cm.