Analysis of the Resonance Column Experiment

1. Principle of Resonance: The resonance column apparatus consists of a tube partially filled with a liquid (usually water), with an air column of variable length above it. The air column acts as a closed organ pipe (closed at the water surface, open at the top). When a tuning fork of a known frequency is held over the open end, it sends sound waves down the air column. These waves reflect off the water surface. At certain specific lengths of the air column, the incident and reflected waves interfere to produce standing waves, resulting in a loud sound. This phenomenon is called resonance.

2. Conditions for Resonance: For a pipe closed at one end, resonance occurs when the length of the air column, $L$, is approximately an odd multiple of a quarter wavelength $(\lambda/4)$. $L_n \approx (2n-1)\frac{\lambda}{4}, \quad \text{for } n = 1, 2, 3, \dots$

   • The first resonance occurs at $L_1 \approx \frac{\lambda}{4}$.
   • The second resonance occurs at $L_2 \approx \frac{3\lambda}{4}$.
   • And so on.

Evaluation of the Options

• Option A: prongs of the tuning fork are kept in a vertical plane A tuning fork's prongs vibrate in a plane perpendicular to their length. If the prongs are held in a vertical plane (i.e., the prongs themselves are vertical), they will vibrate in a horizontal plane. This horizontal vibration of the prongs just above the mouth of the tube creates compressions and rarefactions in the air. These pressure disturbances propagate as sound waves in all directions, including downwards into the resonance tube. This is the standard and correct way to hold the tuning fork in this experiment to effectively excite the air column into resonance without causing excessive turbulence.

• Option B: prongs of the tuning fork are kept in a horizontal plane If the prongs are held in a horizontal plane, they will vibrate in a vertical direction. While this would directly push air into and out of the tube, it is not the preferred method. This can create significant air currents (wind) which can interfere with the formation of a clear standing wave and make it difficult to accurately locate the point of maximum resonance. The standard experimental procedure is described in option A.

• Option C: in one of the two resonances observed, the length of the resonating air column is close to the wavelength of sound in air The first two resonant lengths are $L_1 \approx \lambda/4$ and $L_2 \approx 3\lambda/4$. Neither of these is close to the full wavelength, $\lambda$. Therefore, this statement is incorrect.

• Option D: in one of the two resonances observed, the length of the resonating air column is close to half of the wavelength of sound in air The first two resonant lengths are $L_1 \approx 0.25\lambda$ and $L_2 \approx 0.75\lambda$. Neither of these is close to half the wavelength, $\lambda/2 = 0.5\lambda$. Therefore, this statement is also incorrect.

Conclusion

Based on the analysis, the only correct statement is A, which describes the standard experimental procedure for orienting the tuning fork. Options C and D are physically incorrect regarding the conditions for resonance in a closed pipe. Option B describes a non-standard and less effective way of performing the experiment.