In a resonance column experiment the frequency of tuning fork used is `1000Hz` and the length of pipe is `100m`. Ignoring end correction find the length (in cm) of air column at which second resonance is observed. [Take speed of sound `=330m//s`]

Explanation

To find the length of the air column at which the second resonance is observed in a resonance column experiment, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Resonance Condition**:
In a closed organ pipe, the resonant wavelengths correspond to odd multiples of \( \frac{\lambda}{4} \). The first resonance occurs at \( \frac{\lambda}{4} \), the second resonance occurs at \( \frac{3\lambda}{4} \), and so on. For the second resonance, we have:
\[ L = \frac{3\lambda}{4} \]

2. **Find the Wavelength**:
The relationship between the speed of sound \( v \), frequency \( f \), and wavelength \( \lambda \) is given by:
\[ v = f \lambda \]
Rearranging this gives:
\[ \lambda = \frac{v}{f} \]
Given that the speed of sound \( v = 330 \, \text{m/s} \) and the frequency \( f = 1000 \, \text{Hz} \), we can calculate the wavelength:
\[ \lambda = \frac{330 \, \text{m/s}}{1000 \, \text{Hz}} = 0.33 \, \text{m} \]

3. **Calculate the Length for Second Resonance**:
Using the wavelength found, we can now find the length of the air column for the second resonance:
\[ L = \frac{3\lambda}{4} = \frac{3 \times 0.33 \, \text{m}}{4} = \frac{0.99 \, \text{m}}{4} = 0.2475 \, \text{m} \]

4. **Convert Length to Centimeters**:
Since the question asks for the length in centimeters, we convert meters to centimeters:
\[ L = 0.2475 \, \text{m} \times 100 \, \text{cm/m} = 24.75 \, \text{cm} \]

### Final Answer:
The length of the air column at which the second resonance is observed is \( 24.75 \, \text{cm} \).

---