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 1: Understand the configuration of the pipe
When both ends of the pipe are open, the ends are antinodes. The fundamental frequency (first harmonic) will have one node in the middle and two antinodes at the ends.

### Step 2: Visualize the pipe
Draw a diagram of the pipe:
- Mark the length of the pipe as 2 meters.
- Indicate the two ends as antinodes (A) and the middle point as a node (N).

```
A ------ N ------ A
```

### Step 3: Relate the length of the pipe to the wavelength
In the case of a pipe open at both ends, the relationship between the length of the pipe (L) and the wavelength (λ) of the fundamental frequency is given by:
\[ L = \frac{\lambda}{2} \]

### Step 4: Substitute the known length
Given that the length of the pipe (L) is 2 meters:
\[ 2 = \frac{\lambda}{2} \]

### Step 5: Solve for the wavelength
To find λ, multiply both sides by 2:
\[ \lambda = 2 \times 2 \]
\[ \lambda = 4 \text{ meters} \]

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

---