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I think this has to do with sync of the oscilation of the glass molecules and the air molecules. When the planes passes over your house the air molecules approach the frequency that the glass moleculs oscilate, thus making the amplitude of oscilation bigger. That is why the glass vibrates.

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It's difficult to tell without seeing the whole thing, but ... If it is ultra(low)-sound it means that the driver for your horn should be very large - like over 15-inch to produce high volume with small displacement of the driver. Small displacement of the driver is critical for producing (in normal working conditions) vibrations of air - which are wave - ...

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1) Assuming your coordinates are the motions of the ends of the arms, the equations as you've written them don't allow for any center of mass motion, or at any rate any COM acceleration. I think you want something of the form $$m_{eq}\ddot{x}_1+k_{eq}(x_1-x_5)+c(\dot{x}_1-\dot{x}_5)=F_1(t)$$ And then good old Newtonian summation relates COM motion to net ...

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I think you've got it right. The air space above the liquid creates a chamber that supports resonance at specific frequencies, similar to a flute. Since the chamber may be oddly shaped, it will in general support multiple frequencies or a range of frequencies (unlike a flute, which is designed to resonate at only one frequency). However, since at least ...

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For example an object can vibrate in one dimension only (e.g $x$, thus $1$ degree of freedom). Or an object can vibrate in 2 dimensions (e.g $x$ and $y$, $2$ degrees of freedom) Furthermore an object can vibrate in a rotational sense, a further degree of freedom (in this case an angle lets say $\phi$, in a classical sense and not a quantum-mechanic sense). ...

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