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So recently I came to know that when a wave is produced in string connected to flexible boundary(a ring on a rod) has an amplitude 2 times the amplitude at the end.

I was wondering if it would be possible to connect another string to the same ring from the other side and use the rings movement to produce a wave in that string

If so, on continuously repeating this there should be an exponential increase in amplitude.

It's just a thought and chances are it's wrong because if it is correct it has a lot of applications and people would have discovered this earlier.

It would be appreciated if someone could explain why this wouldn't work

PS: I know 2A is theoretically and practically not possible still there would be an exponential increase which is enough

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  • $\begingroup$ Can you specify how the wave is produced and at which location of the string the amplitude is half than at the end? $\endgroup$
    – user130529
    Commented Feb 6, 2017 at 14:30
  • $\begingroup$ If you attach a string to the other side of the ring, the ring is no longer a boundary. It would be the same as just having a ring tied in the middle of the string, which obviously should have no positive affect on the amplitude. $\endgroup$
    – Asher
    Commented Feb 6, 2017 at 14:30
  • $\begingroup$ @ Asher The "ring at the end" is often used to illustrate a Neumann boudary condition (no perpendicular force, hence tangential is zero). $\endgroup$
    – user130529
    Commented Feb 6, 2017 at 14:34
  • $\begingroup$ @claude chuber so does it work? $\endgroup$
    – Hari07
    Commented Feb 6, 2017 at 14:40
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    $\begingroup$ Sorry, but this is too vague, it is not possible to find an answer to a problem which is not precisely stated, at least what are your initial conditions? Regarding the amplitude, it cannot be constant along the string (unless the string is still), nor suddenly jump at the end. Maybe you can provide a reference? $\endgroup$
    – user130529
    Commented Feb 6, 2017 at 14:57

1 Answer 1

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The (massless) ring at the end of the string is there to have a free end to the string.p i.e. There is no force exerted on the string due to anything on the other side of the ring.
The doubling of amplitude is due to the wave being reflected from such an open end and nothing transmitted.
Adding another string on the other side of the ring means that now there is a force exerted on the string and that as well as the wave being reflected it can also be transmitted with the amplitude at the boundary between the two strings no longer being doubled.
If the added string was the same as that already there then no reflection will occur at the interface.

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