A rope is attached at one end to a fixed vertical pole . It is stretched horizontal with a fixed value of tension `T` . Suppose at `t=0`, a pulse is generated by moving the free end of the rope up and down once with your hand. The pulse arrives at the pole at instant `t`.
Ignoring the effect of gravity, answer the following quetions.
A.. If you move your hand up and down once but to a greater distance and in the same amount of time.

Options

A. Time taken for the pulse to reach the pole will increase and it will be doubled
B. Time taken for the pulse to reach the pole will deacrease and it will become half
C. Time taken for the pulse to reach the pole will not change
D. Cannot change

Explanation

To solve the problem, we need to analyze how the movement of the hand affects the characteristics of the wave pulse generated in the rope.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- A rope is fixed at one end to a pole and stretched horizontally with a constant tension \( T \).
- At \( t = 0 \), a pulse is generated by moving the free end of the rope up and down.

2. **Characteristics of the Pulse**:
- The pulse travels along the rope at a certain speed, which is determined by the tension in the rope and the mass per unit length of the rope.
- The speed of the wave pulse \( v \) can be expressed as:
\[ v = \sqrt{\frac{T}{\mu}} \]
where \( \mu \) is the mass per unit length of the rope.

3. **Effect of Hand Movement**:
- If you move your hand up and down to a greater distance but in the same amount of time, you are increasing the amplitude of the pulse.
- The amplitude of the wave does not affect the speed of the wave pulse; it only affects how "tall" or "strong" the wave appears.

4. **Time Taken for the Pulse to Reach the Pole**:
- Since the speed of the wave pulse remains constant and the distance the pulse travels (from the free end to the pole) does not change, the time taken for the pulse to reach the pole is determined by the formula:
\[ t = \frac{s}{v} \]
where \( s \) is the distance and \( v \) is the speed of the wave.
- As both \( s \) and \( v \) are constant, the time \( t \) will also remain constant.

5. **Conclusion**:
- The time taken for the pulse to reach the pole will not change, regardless of the increased amplitude of the pulse.

### Final Answer:
The time taken for the pulse to reach the pole will remain the same.

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