Question

Problem 15

Answer 1

Given information

Given:

If a rope has a free end, a pulse sent down the rope behaves differently on reflection than if the rope has that end fixed in position. Determine what is the difference and why does it occur.

Step-by-step explanation

Step 1.

When an incident pulse travels through a medium (a string) and reaches a fixed end, a portion of the energy is reflected back to the string in the form of a reflected pulse, while the rest is absorbed by the fixed end (for example, a wall or support).

When an incident pulse propagates via a fixed end string and reaches that point, it is reflected. In relation to the occurrence, the reflected pulse is inverted. Because the methods of propagation are the same, its speed changes direction but its module remains constant. Newton's Third Law explains the inversion of the pulse: the pulse exerts an upward force on the fixed end, and subsequently, it must exert a reaction force of equal size and in the opposite direction on the rope (downward).

The incident pulse travels when the end of the rope is free (which may be imitated with a ring on a rod with little friction), and it is reflected without inverting when it reaches the ring. The propagation speed is the same in each module; the only difference is the direction of propagation.

 

When the pulse reaches the free end of the rope, it exerts a force on it, causing the end to speed upwards. The free end rises to the height of the incoming pulse before being pulled back down by the downward component of the force of tension. The reflected pulse will not reverse and will have the same amplitude as the entering pulse as a result of the end movement.