Two pulses travel in mutually opposite directions in a string with a speed of `2.5 cm//s` as shown in the figure. Initially the pulses are `10 cm` apart. What will be the state of the string after two seconds?

Options

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Answer

To solve the problem, we need to determine the position of the two pulses after 2 seconds, given their initial separation and speed.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Speed of each pulse, \( v = 2.5 \, \text{cm/s} \)
- Initial distance between the two pulses, \( d = 10 \, \text{cm} \)
- Time, \( t = 2 \, \text{s} \)

2. **Calculate the Distance Traveled by Each Pulse:**
- The distance traveled by each pulse in time \( t \) can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- For \( t = 2 \, \text{s} \):
\[ \text{Distance} = 2.5 \, \text{cm/s} \times 2 \, \text{s} = 5 \, \text{cm} \]

3. **Determine the Final Positions of the Pulses:**
- Since the pulses are moving towards each other, each pulse will cover a distance of 5 cm.
- Initially, they are 10 cm apart. After 2 seconds:
- The left pulse moves 5 cm towards the right.
- The right pulse moves 5 cm towards the left.
- Therefore, the new distance between the two pulses will be:
\[ 10 \, \text{cm} - (5 \, \text{cm} + 5 \, \text{cm}) = 0 \, \text{cm} \]
- This means the two pulses will meet and overlap completely.

4. **State of the String After 2 Seconds:**
- When two identical pulses overlap, they interfere with each other. If they are of the same amplitude and shape, they will cancel each other out at the point of overlap.
- Thus, the resultant amplitude at the point of overlap will be 0, and the string will appear straight at that position.

5. **Conclusion:**
- After 2 seconds, the state of the string will be such that the two pulses overlap completely, resulting in a straight line with no displacement.

### Final Answer:
The state of the string after 2 seconds will be a straight line (resultant amplitude = 0).

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