A pulse of a wavetrain travels along a stretched string and reaches the fixed end of the string. It will be reflected back with

Options

A. a phase change of `180^(@)` with velocity reversed.
B. the same phase as the incident pulse with no reversal of velocity
C. a phase change of `180^(@)` with no reversal of velocity.
D. the same phase as the incident pulse but with velocity reversed.

Explanation

To solve the question regarding the reflection of a pulse from a fixed end of a stretched string, we can break it down into the following steps:

### Step 1: Understanding the Situation
A pulse travels along a stretched string and reaches a fixed end. At this point, we need to analyze what happens to the pulse upon reaching the fixed boundary.

**Hint:** Consider what happens to waves when they encounter a boundary.

### Step 2: Reflection at a Fixed End
When a wave pulse reaches a fixed end, it cannot move past the boundary. Instead, it gets reflected back. This reflection is characterized by a change in direction.

**Hint:** Think about how a ball behaves when it hits a wall.

### Step 3: Phase Change
At a fixed end, the wave undergoes a phase change of 180 degrees upon reflection. This means that if the wave was initially moving upwards (positive displacement), after reflection, it will move downwards (negative displacement).

**Hint:** Visualize the wave before and after it hits the fixed end. How does the shape change?

### Step 4: Velocity Change
When the wave reflects off the fixed end, its velocity is also reversed. This means that if the wave was moving in the positive direction towards the fixed end, after reflection, it will move in the negative direction away from the fixed end.

**Hint:** Remember that the direction of velocity is tied to the direction of the wave's movement.

### Step 5: Conclusion
Combining the observations from the previous steps, we conclude that when a pulse of a wave train reaches the fixed end of a string, it will be reflected back with a phase change of 180 degrees and its velocity will be reversed.

**Final Answer:** The pulse will be reflected back with a phase change of 180 degrees and velocity reversed.

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