Describe the experimental setup to determine the speed of sound in air using a resonance column apparatus.

Here is the breakdown for STATION-2: Determination of the Speed of Sound in Air.

STATION-2: DETERMINATION OF THE SPEED OF SOUND IN AIR

Diagram: (2 marks)

\begin{tikzpicture}[scale=0.8] % Measuring cylinder \draw[thick] (0,0) -- (0,4) -- (2,4) -- (2,0) -- cycle; \draw[thick] (0,0) arc (180:360:1 and 0.2); \draw[thick] (0,4) arc (180:360:1 and 0.2); \draw[thick, fill=blue!20] (0,1) arc (180:360:1 and 0.2) -- (2,1) -- (2,0) -- (0,0) -- cycle; \node at (1,-0.5) {Measuring Cylinder}; \node at (2.5, 0.5) {Water}; % Plastic pipe \draw[thick] (0.7, 1) -- (0.7, 5.5) -- (1.3, 5.5) -- (1.3, 1) -- cycle; \draw[thick] (0.7, 5.5) arc (180:360:0.3 and 0.1); \node at (1, 6) {Plastic Pipe}; % Air column length L \draw[dashed] (0.5, 1.2) -- (1.5, 1.2); \draw[<->] (1.5, 1.2) -- (1.5, 5.3); \node at (1.8, 3.25) {$L$}; \node at (1.5, 5.3) {Open end}; % Tuning fork \draw[thick] (2.5, 5.5) -- (2.5, 6.5); \draw[thick] (2.5, 6.5) arc (90:270:0.2 and 0.5); \draw[thick] (2.5, 6.5) -- (2.5, 7.5); \draw[thick] (2.5, 7.5) -- (2.7, 7.5); \draw[thick] (2.7, 7.5) -- (2.7, 6.5); \draw[thick] (2.7, 6.5) -- (2.5, 6.5); \draw[thick] (2.5, 7.5) -- (2.3, 7.5); \draw[thick] (2.3, 7.5) -- (2.3, 6.5); \draw[thick] (2.3, 6.5) -- (2.5, 6.5); \node at (2.5, 8) {Tuning Fork ($f$)}; % Sound waves \draw[decorate,decoration={snake,amplitude=.5mm,segment length=2mm,post length=1mm}] (2.2, 7) -- (1.3, 5.3); \draw[decorate,decoration={snake,amplitude=.5mm,segment length=2mm,post length=1mm}] (2.8, 7) -- (1.3, 5.3); \end{tikzpicture}

Procedure: (2 marks)

1. Fill the measuring cylinder with water.
2. Place the plastic pipe vertically into the water, ensuring its open end is above the water surface.
3. Strike the tuning fork (of known frequency, $f$) gently and hold it horizontally just above the open end of the pipe.
4. Slowly raise the plastic pipe out of the water (or lower the water level) while listening for the loudest sound (resonance).
5. When the first loud sound is heard, measure the length of the air column, $L_1$, from the water surface to the top of the pipe using the metre rule.
6. Repeat steps 3-5 to obtain several readings for $L_1$ and calculate the average.

Observations: (2 marks)

• Frequency of the tuning fork, $f = \_\_\_\_\_$ Hz
• Length of the air column for the first resonance, $L_1 = \_\_\_\_\_$ m (or cm)
• Internal diameter of the plastic pipe, $d = \_\_\_\_\_$ m (or cm)
• (Optional) Room temperature, $T = \_\_\_\_\_ \text{°C}$

Processing: (2 marks)

1. Calculate the end correction, $e$, using the formula: $$e = 0.3d$$ where $d$ is the internal diameter of the pipe.
2. Calculate the corrected length of the air column, $L_c$: $$L_c = L_1 + e$$
3. Determine the wavelength, $\lambda$, of the sound wave. For the first resonance in a closed pipe, the length of the air column is approximately one-quarter of the wavelength: $$\lambda = 4L_c$$
4. Calculate the speed of sound in air, $v$, using the wave equation: $$v = f\lambda$$ Substitute the values of $f$ and $\lambda$ to find $v$.

Precaution: (1 mark)

• Ensure the tuning fork is struck gently to avoid overtones.
• Hold the vibrating tuning fork horizontally and close to the mouth of the pipe.
• Ensure the plastic pipe is held vertically to maintain a uniform air column.
• Take multiple readings for the resonance length and calculate the average to minimize random errors.
• Avoid parallax error when reading the length of the air column from the metre rule.

Conclusion: (1 mark)
The speed of sound in air at the experimental temperature was determined to be $\boxed{\text{calculated value} \text{ m/s}}$.