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emailanmol
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Hello all,
Now imagine this wave traveling (towards right as velocity is positive) and meeting up with
two cases
Case 1) Rigid wall.
Case 2) Free end.
The way gets reflected completely( ignoring transmission or any other losses).
Now my question is what is the new equation of wave.?
for equation of wave as Y=Asin(kx-wt+∅), reflected wave (from free end) is written as Y=Asin(wt+kx+∅) and (for rigid we add a phase difference of pi) to make it y=Asin(wt+kx+∅+pi).
From what I realize this is simply done to make the velocity negative.
Now my question is we could have made the velocity negative even by writing the equation as y=Asin(-kx-wt+∅) (for free end) and y=Asin(-kx-wt+∅+pi) for rigid end.
What prompts us to use the earlier mentioned equations more?
whose coefficient has to be negated to form the reflected wave and why is it so?
Also we could represent the original wave by Y=Asin(wt-kx+∅2) {∅2 is a different phase constant}
In this case what will be the equation of reflected wave(from free end)?
Will it be y=Asin(wt+kx+∅2)
or y =Asin(-wt-kx-∅2)
Thanks a ton
Homework Statement
We can represent a mechanical transverse wave by Y=Asin(kx-wt+∅).Now imagine this wave traveling (towards right as velocity is positive) and meeting up with
two cases
Case 1) Rigid wall.
Case 2) Free end.
The way gets reflected completely( ignoring transmission or any other losses).
Now my question is what is the new equation of wave.?
The Attempt at a Solution
In all textbooks I have studied with, (Resnick Halliday Krane being one of them)for equation of wave as Y=Asin(kx-wt+∅), reflected wave (from free end) is written as Y=Asin(wt+kx+∅) and (for rigid we add a phase difference of pi) to make it y=Asin(wt+kx+∅+pi).
From what I realize this is simply done to make the velocity negative.
Now my question is we could have made the velocity negative even by writing the equation as y=Asin(-kx-wt+∅) (for free end) and y=Asin(-kx-wt+∅+pi) for rigid end.
What prompts us to use the earlier mentioned equations more?
whose coefficient has to be negated to form the reflected wave and why is it so?
Also we could represent the original wave by Y=Asin(wt-kx+∅2) {∅2 is a different phase constant}
In this case what will be the equation of reflected wave(from free end)?
Will it be y=Asin(wt+kx+∅2)
or y =Asin(-wt-kx-∅2)
Thanks a ton
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