What is the fundamental frequency of a closed pipe of length 25 cm filled with carbon dioxide. Velocity of sound in `CO_2` is 266 `ms^(-1).`

Answer

To find the fundamental frequency of a closed pipe, we can use the formula for the fundamental frequency of a closed pipe, which is given by:

\[ f = \frac{v}{4L} \]

where:
- \( f \) is the fundamental frequency,
- \( v \) is the velocity of sound in the medium,
- \( L \) is the length of the pipe.

### Step-by-Step Solution:

1. **Identify the given values:**
- Length of the pipe, \( L = 25 \, \text{cm} = 0.25 \, \text{m} \) (convert cm to m by dividing by 100).
- Velocity of sound in carbon dioxide, \( v = 266 \, \text{m/s} \).

2. **Substitute the values into the formula:**
\[ f = \frac{v}{4L} = \frac{266 \, \text{m/s}}{4 \times 0.25 \, \text{m}} \]

3. **Calculate the denominator:**
\[ 4L = 4 \times 0.25 = 1 \, \text{m} \]

4. **Now substitute back into the frequency formula:**
\[ f = \frac{266 \, \text{m/s}}{1 \, \text{m}} = 266 \, \text{Hz} \]

5. **Conclusion:**
The fundamental frequency of the closed pipe filled with carbon dioxide is \( 266 \, \text{Hz} \).