Longitudinal Waves Help Wanted

[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.

 

[Valerie Park]

Thank you. Yes, the displacement of the sand particles will be an equation like y(x,t)=..., but the factors in the equation will be different than for the longitudinal wave. The equation for the displacement of the sand particles will depend on the mass, volume, and diameter of the particle, as well as the frequency, intensity, and direction of the wave. The equation will also take into account the forces acting on the particles, such as gravity, buoyancy, and viscous drag. The magnitude of the displacement will be proportional to the size of the particle, with smaller particles having a greater displacement than larger particles.

 

[sir-pinski]

It is correct that in a longitudinal wave, the displacement of particles is parallel to the direction of wave propagation. In the case of water, the particles would move back and forth in the same direction as the wave. However, when other particles such as sand are present, their behavior will depend on various factors such as their mass, volume, and diameter.

The displacement equation for these particles can be written as y(x,t)=A*sin[2*π*f*(t-x/u)]*f(M,V,D), where f(M,V,D) represents the function that takes into account the mass, volume, and diameter of the particles. This function will determine how the particles will oscillate in response to the longitudinal wave passing through them.

As you mentioned, the displacement of the particles will not be zero, but it will depend on the size of the particles. Smaller particles with a smaller diameter will experience a larger displacement compared to larger particles. This is because the force exerted by the wave on the particles will depend on their size and mass.

In the case of a rock with a diameter of 5 cm, the displacement may be close to zero because of its large size and mass. However, for a particle with a diameter of 1.e-07 m, the displacement will not be zero as it is much smaller in size and mass.

I hope this helps to clarify your understanding of how longitudinal waves affect particles with different sizes and properties. If you have any further questions, please feel free to ask.