Two pulses having equal and opposite displacements
moving in oppositee directions overlap at `t = t_(1)` sec.
The resultant displacement of the wave at `t=t_(1)` sec is

Options

A. twice the displacement of each pulse
B. half the displacement of each pulse
C. zero
D. Either (a) or (c )

Explanation

To solve the problem of two pulses having equal and opposite displacements moving in opposite directions, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Pulses**: We have two pulses that are equal in amplitude but have opposite displacements. Let's denote the amplitude of the first pulse as \( A \) (moving in the positive direction) and the second pulse as \( -A \) (moving in the negative direction).

2. **Identify the Time of Overlap**: The pulses overlap at \( t = t_1 \) seconds. At this moment, we need to find the resultant displacement of the wave.

3. **Apply the Principle of Superposition**: According to the principle of superposition, when two waves overlap, the resultant displacement is the algebraic sum of the individual displacements.

\[ y_{\text{resultant}} = y_1 + y_2 \]

Here, \( y_1 = A \) (displacement of the first pulse) and \( y_2 = -A \) (displacement of the second pulse).

4. **Calculate the Resultant Displacement**: Substitute the values of \( y_1 \) and \( y_2 \) into the equation:

\[ y_{\text{resultant}} = A + (-A) = A - A = 0 \]

5. **Conclusion**: The resultant displacement of the wave at \( t = t_1 \) seconds is \( 0 \).

### Final Answer:
The resultant displacement of the wave at \( t = t_1 \) seconds is \( 0 \).

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