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The tension is constant in a stationary string. It varies inside the wave.

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Thanx, but it seems that I couldn't explain what I meant. Let me explain with attached picture (pls. see it). In halliday book the 1st picture is used for deriving the speed of a wave, he has considered the specified two tensions (which are shown with F) to be equal.

The 2nd picture has been used for deriving the general equation of a wave; Halliday has considered the specified two tensions (which are shown with F) to be equal, just like the previous part.

Well, here (3rd picture) the problem comes in; Halliday has explained that the tension in part one is not equal with the tension in part two, as a result the potential energies differ from each other.

Now I have mixed up completely, really I don’t know where the tensions are equal and where they aren't.

The 2nd picture has been used for deriving the general equation of a wave; Halliday has considered the specified two tensions (which are shown with F) to be equal, just like the previous part.

Well, here (3rd picture) the problem comes in; Halliday has explained that the tension in part one is not equal with the tension in part two, as a result the potential energies differ from each other.

Now I have mixed up completely, really I don’t know where the tensions are equal and where they aren't.

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