Lets assume we create a standing wave in a cylindrical cavity full of air or water. If we put an escape/exhaust valve at each anode of the wave could we create thrust from the force of the wave acting on the air or a fluid in the cylinder? How much force could we produce? Would resonance also come into play? Also would the node create a vacuum or negative pressure so we could replenish the air or fluid in the cylinder? Would other forms of EMR produce similar effects. Would a coherent laser create a pressure at the anode. I suppose a sound wave could work. Which type of wave would be best? Perhaps a longitudinal pressure wave would work better?
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$\begingroup$ Mars is "next step" who is in? $\endgroup$– StarDrop9Commented Oct 9, 2015 at 20:20
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$\begingroup$ If you ding it why don't you explain it. This is a lot more important than you can envision at this time. $\endgroup$– StarDrop9Commented Oct 9, 2015 at 20:43
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Simple answer: the pressure from a plane wave normally incident on and perfectly reflected by a surface is $2\,I/c$ where $I$ is the wave's intensity; this comes either directly from an electromagnetic calculation for the incidence of a plane wave on a conductor in the $\sigma\to 0$ limit, or, more simply, from the meaning of the momentum four-vector. So, you can work out the thrust from your wave. The intensity in turn is given by $\mathcal{Z}_0^{-1}\,|\vec{E}|^2$, where $\vec{E}$ is the rms electric field vector (complex amplitude) and $\mathcal{Z}_0$ the wave impedance (characteristic impedance) of the medium.
The limiting factor will be the dielectric breakdown electric field $E_{max}$ of the gas in the cylinder, but this will be frequency dependent.
An example: with a 1 watt laser focussed through a 0.3NA objective, the focal point diffraction limited waist area is about $1{\rm \mu\,m}$ across. So the intensity is about $10^{12}{\rm W\,m^{-2}}$ and therefore the pressure is of the order of $3000{\rm Pa}$ - about a thirtieth of an atmosphere.
answered Oct 9, 2015 at 22:08
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$\begingroup$ How would you calculate the pressure if you use sound wave instead of laser EMR wave? $\endgroup$ Commented Oct 12, 2015 at 13:35
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$\begingroup$ @StarDrop9 That is another question in itself as it is quite different from the EM case. A sound wave's intensity is $p\,v$ where $p$ is the pressure and $v$ the Particle Velocity. Superficially, this is like $I = p\, c$ for the EM wave, but the particle velocity is different from the wave velocity, as detailed in the Wiki article. $\endgroup$ Commented Oct 12, 2015 at 21:55
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$\begingroup$ OK you got me. The real questions is. Can a Standing Sound Wave enclosed in a cylinder provide enough lift to negate the force of gravity to lift a starship? This is what I am really looking for and since I know it is true but need to be cautious about being to obvious I ask you for the mathematics. I know how interested you are in What causes a plan to fly... this is much more fun. Again at each node we will create a low pressure zone above craft and at each Anode a high pressure downward thrust. Looking for Ggaravity <= I thrust +;- low pressure effect. Let me know if you need a bounty. $\endgroup$ Commented Oct 13, 2015 at 14:50
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$\begingroup$ just to give practical example, in Electromagnetic levitation of micro-scale actuators using microwave cavity resonators they generate 30 micronewtons of thrust with 1W power in 2cm resonator with Q=20000 Electric Field 3kV/cm and 2 micro joule enclosed energy $\endgroup$ Commented Oct 4, 2016 at 6:58