The wavelength of the fundamental note produced by a pipe of length 2m, when its both ends are open is

Options

A. 2 m
B. 4 m
C. 1 m
D. 8 m

Answer

To find the wavelength of the fundamental note produced by a pipe of length 2 meters with both ends open, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Open Pipes**:
- In an open pipe, both ends are open to the air, which allows the formation of standing waves. The fundamental frequency (first harmonic) occurs when there is one antinode at each end of the pipe.

2. **Use the Formula for Fundamental Frequency**:
- The fundamental frequency \( f \) of an open pipe is given by the formula:
\[ f = \frac{v}{2L} \]
where \( v \) is the speed of sound in air (approximately \( 343 \, \text{m/s} \) at room temperature), and \( L \) is the length of the pipe.

3. **Substitute the Given Length**:
- Here, the length \( L \) of the pipe is given as \( 2 \, \text{m} \).
- Substitute \( L = 2 \, \text{m} \) into the frequency formula:
\[ f = \frac{v}{2 \times 2} = \frac{v}{4} \]

4. **Calculate the Wavelength**:
- The wavelength \( \lambda \) is related to the frequency by the formula:
\[ \lambda = \frac{v}{f} \]
- Substitute \( f = \frac{v}{4} \) into the wavelength formula:
\[ \lambda = \frac{v}{\frac{v}{4}} = 4 \, \text{m} \]

5. **Conclusion**:
- Therefore, the wavelength of the fundamental note produced by the pipe is \( 4 \, \text{m} \).

### Final Answer:
The wavelength of the fundamental note produced by a pipe of length 2m, when both ends are open, is **4 meters**.

---