Why does a wave pulse invert when it hits a fixed boundary on a string?

[Jimmy87]

Hi, please could someone explain why a wave pulse traveling down a rope inverts when it strikes a fixed boundary. Is it something to do with conservation of momentum?

 

[CWatters]

Scroll down..

http://www.acs.psu.edu/drussell/Demos/reflect/reflect.html

 

[GregoryS]

There are no any problems with conservation of momentum: if we consider a longitudinal wave, then a wave pulse will push a fixed boundary which pushes the Earth which changes slightly its orbit.

 

[Philip Wood]

At least two ways of understanding it...

(1) Assume (though we don't have to) that the wave is transverse and in the vertical plane, and that the pulse is an upward 'kink' in the rope. When the start of the kink reaches the wall it exerts an upward force on the wall. So what is the direction of the force that the wall exerts on the string (initiating the reflected wave)?

(2) What is the RESULTANT displacement of the string at the wall due to the incident and reflected waves? What therefore must be the direction of the reflected wave at the wall?

 

[PJC01]

Yes, the inversion of a wave pulse when it hits a fixed boundary on a string is related to the principle of conservation of momentum. When a wave pulse travels down a string, it carries a certain amount of momentum with it. This momentum is transferred to the string as the wave pulse moves along it.

When the wave pulse reaches a fixed boundary, it is unable to continue moving in the same direction. This is because the string is fixed and cannot move. As a result, the wave pulse is reflected back in the opposite direction. In order for this to happen, the momentum of the wave pulse must be conserved. This means that the total momentum before and after the reflection must be equal.

In order for the total momentum to remain the same, the reflected wave pulse must have the same magnitude of momentum as the original wave pulse, but in the opposite direction. This results in the inversion of the wave pulse as it reflects off the fixed boundary.

In summary, the inversion of a wave pulse when it hits a fixed boundary is a result of the conservation of momentum. This principle ensures that the total momentum remains the same before and after the reflection, resulting in the wave pulse being reflected back in the opposite direction.