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.
In all the above, quetions we have considered a fixed value of tension. however, if tension in a given rope is increased and a pulse is genrated as described,

Options

A. Time taken for the pulse to reach the pole may increase to decrease
B. Time taken for the pulse to reach the pole will not change
C. Time taken for the pulse to reach the pole will increase
D. Time taken for the pulse to reach the pole will deacrease

Explanation

To solve the problem, we need to analyze how the tension in the rope affects the speed of the wave pulse and subsequently the time it takes for the pulse to reach the fixed pole.

### Step-by-Step Solution:

1. **Understanding Wave Velocity**:
The velocity \( V \) of a wave traveling through a rope is given by the formula:
\[ V = \sqrt{\frac{T}{\mu}} \]
where \( T \) is the tension in the rope and \( \mu \) is the linear mass density of the rope.

2. **Initial Condition**:
Initially, we have a fixed tension \( T \) in the rope. When a pulse is generated, it travels towards the pole with a certain velocity \( V \).

3. **Effect of Increasing Tension**:
If the tension \( T \) in the rope is increased, the velocity \( V \) of the wave pulse will also increase because \( V \) is directly proportional to the square root of the tension:
\[ V_{\text{new}} = \sqrt{\frac{T_{\text{new}}}{\mu}} \]
where \( T_{\text{new}} > T \).

4. **Time Calculation**:
The time \( t \) taken for the pulse to travel a distance \( L \) (length of the rope) is given by:
\[ t = \frac{L}{V} \]
Since \( L \) is constant and \( V \) increases when tension increases, the time taken for the pulse to reach the pole will decrease:
\[ t_{\text{new}} = \frac{L}{V_{\text{new}}} < \frac{L}{V} = t \]

5. **Conclusion**:
Therefore, when the tension in the rope is increased, the time taken for the pulse to reach the pole decreases.

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