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Does resonance have limit?+Fluid

  1. Jan 22, 2013 #1
    I made a helmholtz resonator by myself and played its resonace frequency sound to it. Obviously, the resonator resonated and near the open end of resonator, I could feel wind.
    So I placed candle near the opening to see the strength of wind. Surprisingly, If decibel of soundwave was constant, the candle's movement was constant. Which means, the angle of tilted fire was constant.
    What I thought was that when a material is resonating, It's amplitude of vibration continues to increase although the external soundwave's amplitude is constant. Isn't it true? If it is true, Why was the strength of wind constant? ( the lump of air near opening of Helmholtz resonator also goes under harmonic motion.)( For sure, the lump of air oscillate at resonance frequency.)

    Isn't wind strength a velocity of fluid? So if wind strength is constant, it means that frequency and velocity of lump of air is constant. right??

    other than that, is it the flow rate(N) that affects movement of fire or velocity of fluid?
     
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  3. Jan 22, 2013 #2

    AlephZero

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    You are right that the mathematical solution of an equation like ##x'' + \omega^2 x = F \cos \omega t## increases without limit, but a real resonator always loses energy for some reason. It is described better by an equation like ##x'' + 2\beta\omega x' + \omega^2 x = F \cos \omega t## where ##\beta## is a measure of the amount of energy loss.

    For a Helmholtz resonator, there are two main causes of energy loss:
    (1) The resonator radiates sound energy into the air. Note, that fact is not mentioned in many introductions to sound, when discussing things like the boundary conditions for open and closed pipes! It is the physical reason for the "end correction" of the length of an open pipe resonator.
    (2) The viscosity of the air causes energy loss at the surface of the resonator, where the air velocity is always zero.

    The size of (1) depends mainly on the cross section area of the neck of the resonator. (2) depends on the total surface area of the resonator.
     
  4. Jan 22, 2013 #3
    Thanks!! theres something confusing though;; When length of Open pipe increase, It is sure that the resonance frequency decreases due to friction. However, isn't the effective length, or end correction for Helmholtz Resonator L+1.4r??
    What I think is because the "end correction" range increase as length increase, Although natural frequency decreases, because the amplitude of oscillation is greater, the velocity of air will be great. Am I correct? I am not sure whether longer effective length can be viewed as larger amplitude;;
     
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