Six antinodes are observed in the air column when a standing wave forms in a Kundt's tube . What is the length of the air column if steel bar of ` 1 m` length is clamped at the middle .
The velocity of sound in steel is `5250 m//s` and in air `343 m//s`.

Explanation

To solve the problem, we need to find the length of the air column in the Kundt's tube when 6 antinodes are formed, given that a steel bar of length 1 m is clamped at the middle.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- The steel bar is clamped at the middle, which means it acts as a fixed point for the standing wave. This creates two segments of the bar, each of length 0.5 m.

2. **Wavelength in Steel**:
- The wavelength of the sound in the steel can be calculated using the formula for the wave speed:
\[ v_s = f \lambda_s \]
- Here, \( v_s \) is the velocity of sound in steel (5250 m/s), and \( \lambda_s \) is the wavelength in steel.
- Since the length of the steel bar is 1 m, and it has a node at the center, the wavelength in steel can be expressed as:
\[ \lambda_s = 2 \times \text{Length of the bar} = 2 \times 1 = 2 \text{ m} \]

3. **Finding the Frequency**:
- Using the relationship between the wave speed and wavelength, we can find the frequency:
\[ f = \frac{v_s}{\lambda_s} = \frac{5250 \, \text{m/s}}{2 \, \text{m}} = 2625 \, \text{Hz} \]

4. **Wavelength in Air**:
- The frequency of sound in air will be the same as in steel, so we can use the velocity of sound in air (343 m/s) to find the wavelength in air:
\[ v_a = f \lambda_a \]
- Rearranging gives:
\[ \lambda_a = \frac{v_a}{f} = \frac{343 \, \text{m/s}}{2625 \, \text{Hz}} \approx 0.1305 \, \text{m} \]

5. **Length of the Air Column**:
- We know that 6 antinodes correspond to 6 half wavelengths (since the distance between two consecutive antinodes is \( \frac{\lambda_a}{2} \)):
\[ L_0 = 6 \times \frac{\lambda_a}{2} = 3 \lambda_a \]
- Substituting the value of \( \lambda_a \):
\[ L_0 = 3 \times 0.1305 \, \text{m} \approx 0.3915 \, \text{m} \approx 39.15 \, \text{cm} \]

### Final Answer:
The length of the air column is approximately **39.15 cm**.