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Sound intensity on a flat earth

  1. Feb 15, 2010 #1
    Sound intensity on a "flat earth"

    1. The problem statement, all variables and given/known data

    Consider a flat Earth with an atmosphere that descreases in density as altitude increases such that rho = rho0e-h/H where rho nought is the density of air at zero altitude and H is a constant known as the "scale height". Assume the bulk modulus of air is constant. a)Show that the intensity of a soundwave of constant wavelenght will increase with altitude (assume velocity changes due to a change in frequency only). b) Show that the intensity of a soundwave of constant frequency will decrease with altitude (Assume velocity changes due to a change in wavelenght only). c) Show that the ratio of the dreivatives is given by:
    (dI/dh) lamda constant / (dI/dh) freq. constant = -eh/H

    2. Relevant equations

    I = .5p v w^2 S^2
    p = rho
    w = omega


    3. The attempt at a solution
    I've been breaking my head trying to do this.
    The only thing i can think of is to get all the wanted variables into the equation:

    I = .5p (lambda/time) (2pi f)^2 S^2

    but then how do I go from there?
    I have the feeling that I have to do partial dv/dlambda and partial dv/dfreq.
    but I dont know how and where to insert them and use them.

    ty.
     
  2. jcsd
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