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Longitudinal Wave Help Needed

  1. Aug 26, 2008 #1
    I know that when a Longitudinal (Sound) Wave spreads in water the displacement
    of the water particles is parallel to the direction of wave propagation and the displacement
    equation looks like this :

    y(x,t)=A*sin[2*π*f*(t-x/u)]

    where : A=Amplitude, π=3.14..., f=frequency, u=speed of wave propagation

    If i have diffused in the water some other particles, lets say sand, how will the particles
    of the sand oscillate? I think the displacement should be also an equation like y(x,t)=...
    but now it has to be a function of M (mass), maybe V(volume) and D(particle diameter)
    as well.I believe that if a Longitudinal wave reaches a rock of D=5 cm displacement of
    rock will be almost zero, but if it reaches a particle of D=1.e-07 m displacement will not
    zero.
    If you have any ideas, please reply.
     
  2. jcsd
  3. Aug 26, 2008 #2
    That equation is already is a function of mass, volume and particle diameter (which is related to particle volume). What you are describing is particle density. The speed of the wave is itself a function of media density.

    However, adding sand to water is creating an inhomogenous medium. While you can simplify the particle density into bulk density, if you want to calculate the actual displacement of the sand particles, I think you are going to need a bigger equation.
     
  4. Aug 28, 2008 #3
    That bigger equation I am looking for, but so far nothing.
    Thanks for the reply.
     
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