In a resonance tube experiment to determine the speed of sound in air, a pipe of diameter `5 cm` is used . The column in pipe resonates with a tuning fork of frequency `480 H_(Z)` when the minimum length of the air column is `16 cm` . Find the speed in air column at room temperature.

Explanation

To find the speed of sound in air using the resonance tube experiment, we can follow these steps:

### Step 1: Understand the relationship between frequency, speed, and wavelength
The fundamental frequency of a closed organ pipe can be expressed using the formula:
\[ f = \frac{V}{4L} \]
where:
- \( f \) is the frequency (in Hz),
- \( V \) is the speed of sound (in m/s),
- \( L \) is the length of the air column (in meters).

### Step 2: Convert the given values to appropriate units
The minimum length of the air column is given as 16 cm. We need to convert this to meters:
\[ L = 16 \text{ cm} = 0.16 \text{ m} \]

The frequency is given as:
\[ f = 480 \text{ Hz} \]

### Step 3: Calculate the end correction
The end correction \( e \) for a closed pipe is given by:
\[ e = 0.6 \times R \]
where \( R \) is the radius of the pipe. The diameter of the pipe is given as 5 cm, so the radius is:
\[ R = \frac{5 \text{ cm}}{2} = 2.5 \text{ cm} = 0.025 \text{ m} \]

Now, we can calculate the end correction:
\[ e = 0.6 \times 0.025 \text{ m} = 0.015 \text{ m} \]

### Step 4: Adjust the length of the air column
The effective length \( L' \) of the air column, taking into account the end correction, is:
\[ L' = L + e = 0.16 \text{ m} + 0.015 \text{ m} = 0.175 \text{ m} \]

### Step 5: Substitute the values into the frequency formula
Now we can rearrange the formula for speed \( V \):
\[ V = 4Lf \]
Substituting the values we have:
\[ V = 4 \times 0.175 \text{ m} \times 480 \text{ Hz} \]

### Step 6: Calculate the speed of sound
Calculating this gives:
\[ V = 4 \times 0.175 \times 480 = 336 \text{ m/s} \]

### Final Answer
The speed of sound in the air column at room temperature is approximately:
\[ V \approx 336 \text{ m/s} \]

---