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Two strings connected by a spring

  1. Nov 5, 2015 #1
    avatar_m.png 55 Hi all,

    Hello,

    Racking my brains over this :

    If I have two semi-infinite strings (made of same material) - which are connected by a massless spring, and now I send a longitudinal wave along one string.

    Will the spring just pass on the wave to the other string or will it serve to reflect some of it back ?

    If it does reflect some of it back, what would be the boundary conditions that you will have to impose ?

    Is it just that the E * du/dx which is the stress in the two strings, should be equal to k*(u1 - u2) where u1 and u2 are the displacements of the two strings at the interface between the string and the spring ? So I will just have:

    E * du1 /dx = -k * (u1 - u2)
    E * du2 /dx = k * (u1 - u2)

    One of the right hand sides is of opposite sign as the direction of force is opposite.

    Not able to show energy conservation with this. Perhaps I am using the wrong boundary conditions ?

    Thanks!

    Thanks!
     
  2. jcsd
  3. Nov 5, 2015 #2

    davenn

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    what do you think and why ?


    Dave
     
  4. Nov 5, 2015 #3
    When the spring compresses as the wave reaches it, it exerts a force back at the thread. This would cause some of the momentum of the wave to change direction. So it should be reflected partly...?
     
  5. Nov 5, 2015 #4

    berkeman

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    Staff: Mentor

    Waves in strings are usually transverse. How do you effectively couple a longitudinal wave onto a string? Do you have a physical system in mind with this question?
     
  6. Nov 5, 2015 #5
    Maybe something like the can (or paper cup) "telephone". :)
     
  7. Nov 5, 2015 #6

    berkeman

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    Staff: Mentor

    Ah, good point!

    @Karthiksrao -- Are you familiar with the Wave Equation and how it's derived? Also, how long is the weightless spring compared to the wavelength of your longitudinal wavelength? What is the relationship between the spring constant k and the equivalent parameter for the string?
     
  8. Nov 6, 2015 #7
    Yes indeed I am more than familiar with the wave equation and its derivation. The wavelength and length of the spring is of the same order - so the wave sees the spring. Likewise, the spring constant and the material elastic constant are enough to affect each other.

    My point is not to solve a problem with given parameters. That is immaterial.

    What I am trying to figure out is how we can go about approaching this problem, Intuitively I do feel there will be reflection and transmission, but what would be the boundary conditions for a wave at the 'spring interface'

    Many thanks
     
  9. Nov 6, 2015 #8

    davenn

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    have a look at this site
    http://www.physicsclassroom.com/class/waves/Lesson-3/Boundary-Behavior

    scroll down about 1/2 way for
    Transmission of a Pulse Across a Boundary from Less to More Dense

    tho the whole page may be enlightening to you


    Overall, your query is also the basis of impedance mismatches in transmission lines at termination points etc and the losses incurred, standing waves generated etc :smile:
    amongst many other uses ....
    In my seismology studies when doing seismic reflection of sound waves transmitted into the earth
    to determine densities of the different rock layers etc

    you might also be interested in this classic old Bell Labs teaching video
    on wave propagation, reflection etc


    cheers
    Dave
     
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