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Natural Science Forum / Physics / Acoustics / September 2004vibration of particles in sound field
Hi I'm interested in the behaviour of airborne particles in the 0.1 to 10 micron range, in response to sounds from 100Hz to 100KHz. What is the peak velocity of the particles as a function of particle diameter, particle density, sound frequency and sound intensity? Initially I just want a rough idea of the max velocity values - but if anyone can give approximate formulae in terms of the above variables, I would be very grateful. Book and journal references (if not on the web), are not much help because I don't have access to Univ or technical libraries. Thanks > I'm interested in the behaviour of airborne particles in the 0.1 to 10 micron > range, in response to sounds from 100Hz to 100KHz. [quoted text clipped - 7 lines] > Book and journal references (if not on the web), are not much help > because I don't have access to Univ or technical libraries. Wikipedia may help you: http://en.wikipedia.org/wiki/Particle_displacement http://en.wikipedia.org/wiki/Sound_pressure http://www.sengpielaudio.com/calculator-soundlevel.htm http://www.sengpielaudio.com/calculator-ak-ohm.htm http://www.sengpielaudio.com/calculator-speedsound.htm You will not find formulas as a function of particle diameter. Cheer Eberhard Sengpiel http://www.sengpielaudio.com/calculator-soundlevel.htm Thanks for your reply, but I think you have confused the various uses of the word 'particle'. The "sound particle velocity" as conventionally used in acoustics refers to net molecular velocities within a 'particle' of fluid. 'Particle' is something of a misnomer here, as the SPV refers to an infinitesimal volume element of arbitrary geometry, without any actual physical boundaries. In contrast, I am asking about airborne particles of a size verging on the macroscopic (up to 10 microns, as stated). These are 'real' particles with well-defined physical boudaries, and with a different composition from the gas in which they are suspended. They are enormous in size and inertia when compared with gas molecules. I would expect the velocity of these particles to be very different from the "particle velocity" of the gas medium as defined in acoustics. Does anyone know of some actual figures for the velocity of suspended particles in a sound wave? Obviously, particle size and density *will* make quite a difference. Thanks ross ============================================================ >> I'm interested in the behaviour of airborne particles in the 0.1 to 10 >micron [quoted text clipped - 26 lines] > >http://www.sengpielaudio.com/calculator-soundlevel.htm > In contrast, I am asking about airborne particles of a size verging on the > macroscopic (up to 10 microns, as stated). These are 'real' particles with [quoted text clipped - 3 lines] > to be very different from the "particle velocity" of the gas medium as defined > in acoustics. I ran into the same dilemma in my PhD thesis. (JASA 111 May'02 pp 2087-2096). Here, I was contemplating the force that an ion in an electric field will exert onto the water medium. In my discussion between Eq(10) and Eq(11), I concluded that the viscous force dominates at audio and ultrasound frequencies. Somehow, you need to derive or determine the viscous force vs velocity, and likely it will be linear (speed = force times a constant). The common way to get this empirical data is to observe the falling speed under gravity of a particle falling tough the liquid. Somehow you need to weigh the particle, or use other strategies to get the friction vs size and or mass. Then you can apply a linear differential equation of motion, where it should be clear that the oscillating amplitude, or velocity, will be less than the acoustical particle displacement in a manner inversely proportional to frequency squared or frequency, etc. > Does anyone know of some actual figures for the velocity of suspended particles > in a sound wave? Obviously, particle size and density *will* make quite a > difference. Maybe the chem or physics abstracts database may contain some useful data. Angelo Campanella >Somehow, you need to derive or determine the viscous force vs velocity, >and likely it will be linear (speed = force times a constant). The [quoted text clipped - 7 lines] >less than the acoustical particle displacement in a manner inversely >proportional to frequency squared or frequency, etc. That's a help, Angelo. I dug up a site that gives examples of Stokes' law. From that I calculated that a 4 micron diameter water droplet should fall in still air at roughly 0.5 mm/sec. I calculate the mass of this spherule to be 335 ng. I assume that the particle motion will be sinusoidal but a bit out of phase with the sound wave driving it. Are there standard formulae we can use to finish the calculation? I have the general concepts, but no engineering maths background, so can anyone help me finish this off? I want to know what the peak velocity of the droplet's movement will be, for a chosen sound frequency and intensity. If anyone can show me the method, I will work out values for other frequencies and intensities myself. Thanks ross > That's a help, Angelo. I dug up a site that gives examples of Stokes' law. > From that I calculated that a 4 micron diameter water droplet should fall in > still air at roughly 0.5 mm/sec. I calculate the mass of this spherule to be > 335 ng. I assume that the particle motion will be sinusoidal but a bit out of a standard differential equation can be applied. mx,tt + sx,t = f(t) where s is the friction of the motion; force per velocity, and f(t) is the forcing function. Now one has to coin the particle movement in terms of a moving medium and a would be stationary particle. I have run out of ideas on this one. It all requires some serious pondering by we various... Good luck! Angelo Campanella \ > Now one has to coin the particle movement in terms of a moving medium > and a would be stationary particle. I have run out of ideas on this one. > It all requires some serious pondering by we various... In the limit of very constrained motion due to whatever cause, herein lies the real solution to what is called Doppler distortion. What is the force acting on the particle as its ability to move with the air is reduced to zero? The question of the force on constrained particles in moving air is intimately tied to the pressure distortion produced at a fixed point in space as a function of the motion of the air about it. If that point is taken to be the fully constrained rest position of a driving diahragm in a tube, the solution is the correct solution to the question of "Doppler distortion" in that configuration because that is the planar pressure wave that propegates away from it. I can't figure out how to get there from here either. Bob  Signature"Things should be described as simply as possible, but no simpler." A. Einstein > maths background, so can anyone help me finish this off? I want to know what > the peak velocity of the droplet's movement will be, for a chosen sound > frequency and intensity. If anyone can show me the method, I will work out > values for other frequencies and intensities myself. Look up also the "Raleigh Disc". This was a very early sound level detector. raleigh showed that a tiny lightweight disc, mounted on a pivot like a stovepipe damper, will want to align itself with its surface parallel to the airflow. The airflow in this case is the air's acoustic particle velocity. There is a working equation for that device... it was before my time, so we never spent much effort working it.. said equation might help your insight a little. Ang. C. |
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