A stretched string of length 2 m vibrates in 4 segments. The distance between consecutive nodes is

Options

A. 0.5 m
B. 0.25 m
C. 1.0 m
D. 0.75 m

Explanation

To solve the problem of finding the distance between consecutive nodes on a stretched string vibrating in 4 segments, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have a stretched string of length 2 meters that vibrates in 4 segments. We need to find the distance between consecutive nodes.

2. **Identify the Number of Segments**: The string is vibrating in 4 segments. This means that there are 4 sections of the wave along the length of the string.

3. **Determine the Number of Nodes**: For a string vibrating in 'n' segments, the number of nodes (N) is given by:
\[ N = n + 1 \]
In this case, since \( n = 4 \):
\[ N = 4 + 1 = 5 \]
So, there are 5 nodes along the length of the string.

4. **Calculate the Distance Between Nodes**: The total length of the string is 2 meters. The distance between consecutive nodes can be calculated by dividing the total length of the string by the number of segments:
\[ \text{Distance between nodes} = \frac{\text{Length of the string}}{\text{Number of segments}} = \frac{2 \text{ m}}{4} = 0.5 \text{ m} \]

5. **Conclusion**: Therefore, the distance between consecutive nodes is 0.5 meters.

### Final Answer:
The distance between consecutive nodes is **0.5 meters**.