Question

If an incident pulse, moving towards a rigid support is as shown, then among the following (figures in the options), which one represents the reflected pulse correctly?

• A.
• B.
• C.
• D.

Answer 1

Answer: (B)

b

Answer 2

When a wave pulse is reflected from a rigid support (fixed end), it undergoes a phase change of $\pi$. This means that the displacement of the reflected pulse is opposite to the displacement of the incident pulse at the point of reflection. The shape of the pulse is preserved, but it is inverted vertically. The reflected pulse also travels in the opposite direction to the incident pulse.

In the given problem, the incident pulse is moving towards a rigid support on the left. The pulse is shown to the right of the support and is moving towards the left. The shape of the incident pulse, from left to right, is a positive displacement hump followed by a negative displacement trough. Since the pulse is moving towards the left, the leftmost part of the pulse is the leading edge, and the rightmost part is the trailing edge. Thus, the leading edge of the incident pulse is the part with positive displacement, and the trailing edge is the part with negative displacement.

When this pulse reflects from the rigid support, it will be inverted and move towards the right. The leading edge of the incident pulse (positive displacement) will be reflected as a negative displacement and will be the leading edge of the reflected pulse. The trailing edge of the incident pulse (negative displacement) will be reflected as a positive displacement and will be the trailing edge of the reflected pulse.

So, the reflected pulse, moving towards the right, will have a shape that starts with a negative displacement (corresponding to the reflection of the positive hump of the incident pulse) followed by a positive displacement (corresponding to the reflection of the negative trough of the incident pulse).

Let's examine the options: (a) Reflected pulse moving right with a positive hump followed by a negative trough. This is the same shape as the incident pulse, but moving in the opposite direction. This would be the reflection from a free end. (b) Reflected pulse moving right with a negative trough followed by a positive hump. This is the inverted shape of the incident pulse, with the order of the humps reversed due to reflection and change in direction. This matches our expectation. (c) Reflected pulse moving right with a negative trough followed by a shape that does not match the inverted trailing edge. (d) Reflected pulse moving right with a positive hump followed by a shape that does not match the inverted trailing edge.

Therefore, the correct representation of the reflected pulse is shown in option (b). The reflected pulse is inverted and travels in the opposite direction.