Net Displacement of Element on String at Crossing Pulses

[Husker70]

Homework Statement

A series of pulses, each of amplitude 0.150m, are sent down a string that is attached
to a post at one end. The pulses are reflected at the post and travel back along the
string without loss of amplitude. When two waves are present on the same string, the net
displacement of a particular element of the string is the sum of the displacement of the
individual waves at that point. What is the net displacement of an element at a point
on the string where two pulses are crossing (a) if the string is rigidly attached to the post
and (b) if the end at which reflection occurs is free to slide up and down.

Homework Equations

None that I know of


3. The Attempt at a Solution [/c]
(a) if the string is attached to the post without moving the first pulse will travel up
and the reflected pulse with be inverted. As the second pulse with an upward travel
meets an inverted pulse with the same amplitude they will cancel and be zero.
(b) if the string is attached to the post so that it can slide up and down the first
pulse will travel up and the reflected pulse will be upward. As thy meet the net
displacement will be the sums of .150m + .150m = .300m

Does this seem right?
Thanks
Kevin

 

[dpowd]

Husker,
Yes, the problem is as simple as it looks. The big issue is determining the orientation of a wave that's been reflected from a fixed barrier vs that from a free barrier, which you have done correctly. Then, at a point where an incident pulse (of amplitude A) overlaps a reflected pulse, the only possible results are either A + A = 2A, or A + -A = 0. Nice Work.

 

[thomate1]

Yes, your explanation and solution seem correct. In scenario (a), the pulses will cancel each other out due to their opposite amplitudes, resulting in a net displacement of 0. In scenario (b), the pulses will add together, resulting in a net displacement of 0.3m. This is because in scenario (a), the string is fixed at the post so it cannot move, while in scenario (b), the string is free to move, allowing the pulses to add together. This is a good example of how the boundary conditions of a system can affect the behavior of waves.