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Questions regarding equation for circular mode frequency

  1. Dec 7, 2011 #1
    I'm trying to determine the circular mode frequency for an open-ended pipe using the following equation and could use some clarification:

    f = (t/(2*d^2))*SQRT(E/density)

    f - frequency
    E - modulus of elasticity
    d - mean diameter
    t - wall thickness

    My first question is; do I need to multiply the values inside the SQRT by gravity (386.4 in/sec2) in order to get the correct units for this equation?

    Also, is the frequency noted here (f) referring to radian per second and will I need to divide it by 2*pi in order to convert it to cycles per second?

    Any help would be greatly appreciated. Thanks!
  2. jcsd
  3. Dec 7, 2011 #2
    It has the right units as it is. The part with the square root is the speed of sound in the material of the pipe.
  4. Dec 8, 2011 #3


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    You need to use consistent units. SI units (kg/m^3 and Pascals) are consistent. Units that mix up "pounds mass" and "pounds force" are not.

  5. Dec 8, 2011 #4
    Thanks so much for the help on this... I really appreciate it!

    I may be asking the same question twice but can you verify for me if I need to apply the same freq conversion for Hz (/2*pi) to the following equation used to determine transverse waves in a pipe with free ends?



    v= √ (Y/r)
    Y= Young's modulus
    r= density
    K= 1/2 * √ (a^2 + b^2)
    a= inside radii
    b= outside radii
    L= length
    m= 3.0112, 5, 7...(2n+1)
  6. Dec 9, 2011 #5
    This gives the frequency in hertz, according to Ross - Percussion instruments.
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