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Longitudinal standing waves

  1. Oct 16, 2013 #1
    1. The problem statement, all variables and given/known data
    How to find the fundamental frequency of standing longitudinal waves?Are they similar to standing transverse waves?

    2. Relevant equations
    none


    3. The attempt at a solution
    I know pretty much about standing transverse waves in strings. But i am confused about standing longitudinal waves in strings.:confused:
     
  2. jcsd
  3. Oct 16, 2013 #2
    They are similar to standing transverse waves. Think again, similar equations are used.
     
  4. Oct 16, 2013 #3
    The problem statement is-
    A string is stretched so that its length is increased by 1/n of its original length. Find the ratio of fundamental frequency of transverse vibration to that of fundamental frequency of longitudinal vibration.
     
  5. Oct 16, 2013 #4
    Ok i got this question right. Speed of longitudinal wave in strings depends on Young's modulus.
     
  6. Oct 16, 2013 #5
    A string forms transverse wave, not longitudinal wave. maybe the question wants you to assume longitudinal wave traveling through a tube (and its length is increased) and calculate the ratio between the two.

    Edit: great, that you got it!!!.....I guess I overlooked the question, the question was asking about the longitudinal waves that travel through every material medium or maybe longitudinal term was misprinted.
     
    Last edited: Oct 16, 2013
  7. Oct 16, 2013 #6
    BTW, speed of longitudinal waves in general depends on Bulk modulus.
     
  8. Oct 16, 2013 #7
    The term bulk modulus is used for gases and liquids. In metals we use Young's modulus, isn't it?
     
  9. Oct 16, 2013 #8
    Bulk modulus is also used for solids/metal. For tensile stress young's modulus is used, for hydraulic stress bulk modulus is used.

    $$v_{transverse}=\sqrt{\frac{T}{μ}}$$
    $$v_{longitudinal}=\sqrt{\frac{B}{ρ}}$$
    ##T## is Tension.
    ##μ## is linear mass density
    ##B## is Bulk modulus
    ##ρ## is density

    Edit: Tension can be related to young's modulus by:
    $$T=Y.A.\frac{ΔL}{L}$$
    ##Y## is young's modulus
    ##A## is cross-sectional area.
    ##L## is initial length of the string.
     
    Last edited: Oct 16, 2013
  10. Oct 16, 2013 #9
    ....and there goes my 100th post

    thanks
     
  11. Oct 16, 2013 #10
    :thumbs:
     
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