In an organ pipe the distance between the adjacent node is `4 cm`. Find the frequency of source if speed of sound in air is `336 m//s`.

Explanation

To solve the problem step by step, we need to find the frequency of the sound produced by an organ pipe given the distance between adjacent nodes and the speed of sound in air.

### Step-by-Step Solution:

1. **Identify the distance between adjacent nodes**:
The problem states that the distance between adjacent nodes is `4 cm`.

2. **Convert the distance to meters**:
Since the speed of sound is given in meters per second, we need to convert `4 cm` to meters:
\[ 4 \, \text{cm} = 4 \times 10^{-2} \, \text{m} = 0.04 \, \text{m} \]

3. **Relate the distance between nodes to the wavelength**:
In a standing wave, the distance between two adjacent nodes is equal to half the wavelength (\(\lambda\)):
\[ \text{Distance between nodes} = \frac{\lambda}{2} \]
Therefore, we can set up the equation:
\[ 0.04 \, \text{m} = \frac{\lambda}{2} \]

4. **Solve for the wavelength (\(\lambda\))**:
To find \(\lambda\), we can rearrange the equation:
\[ \lambda = 2 \times 0.04 \, \text{m} = 0.08 \, \text{m} = 8 \times 10^{-2} \, \text{m} \]

5. **Use the speed of sound to find frequency**:
The frequency (\(f\)) can be calculated using the formula:
\[ f = \frac{v}{\lambda} \]
where \(v\) is the speed of sound. Given that \(v = 336 \, \text{m/s}\):
\[ f = \frac{336 \, \text{m/s}}{0.08 \, \text{m}} \]

6. **Calculate the frequency**:
Performing the division:
\[ f = \frac{336}{0.08} = 4200 \, \text{Hz} \]

7. **Convert frequency to kilohertz**:
To convert Hertz to kilohertz, divide by 1000:
\[ f = \frac{4200 \, \text{Hz}}{1000} = 4.2 \, \text{kHz} \]

### Final Answer:
The frequency of the source is \(4.2 \, \text{kHz}\).

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