How Does Adding Sand Affect Longitudinal Wave Displacement in Water?

[Carter2x]

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, let's 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.

 

[jaseh86]

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.

 

[Carter2x]

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.

That bigger equation I am looking for, but so far nothing.
Thanks for the reply.