An organ pipe of length 0.4m is open at both ends . The speed of sound in air is `340ms^(-1)` . The fundamental frequency is

Options

A. 400Hz
B. 425Hz
C. 450Hz
D. 475Hz

Explanation

To find the fundamental frequency of an organ pipe that is open at both ends, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Length of the Pipe (L)**:
The length of the organ pipe is given as \( L = 0.4 \, \text{m} \).

2. **Determine the Speed of Sound (v)**:
The speed of sound in air is given as \( v = 340 \, \text{m/s} \).

3. **Understand the Fundamental Frequency in Open Pipes**:
For a pipe open at both ends, the fundamental frequency corresponds to the first harmonic. The wavelength (\( \lambda \)) for the fundamental frequency in such a pipe is given by:
\[ \lambda = 2L \]

4. **Calculate the Wavelength**:
Substitute the length of the pipe into the wavelength formula:
\[ \lambda = 2 \times 0.4 \, \text{m} = 0.8 \, \text{m} \]

5. **Use the Relationship Between Speed, Frequency, and Wavelength**:
The relationship between speed (\( v \)), frequency (\( f \)), and wavelength (\( \lambda \)) is given by:
\[ v = f \cdot \lambda \]
Rearranging this gives us the formula for frequency:
\[ f = \frac{v}{\lambda} \]

6. **Substitute the Values to Find Frequency**:
Now, substitute the values of \( v \) and \( \lambda \):
\[ f = \frac{340 \, \text{m/s}}{0.8 \, \text{m}} = 425 \, \text{Hz} \]

7. **Conclusion**:
Therefore, the fundamental frequency of the organ pipe is \( 425 \, \text{Hz} \).