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The maximum of $$\left|\cfrac{V_2}{V_1}\right| = \cfrac{\sqrt{1+(\omega RC)^2}}{\sqrt{4 + (\omega RC)^2}}$$ is $1$ at $\omega=\pm \infty$, and you find the half power frequency by solving: $$\frac{1+(\omega RC)^2}{4+(\omega RC)^2}=\frac{1}{2}$$ which gives $\omega=\pm \sqrt{2}/RC$

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As a planetary science and aviation enthusiast I can offer these tidbits, although a bit late for the 2013 posted question.... http://www.wired.com/2010/05/gallery-clouds/ This shows mountain-induced Van Karman vortex street (Strouhal instability) in a cloud layer as viewed from space. and so does this: ...

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By adding the rubber band you did two things: increased the air drag unbalanced the fan The bearings of a fan don't like to be unbalanced - the friction goes up significantly because as the fan picks up speed there will be a large lateral force (centripetal force keeping the rubber band plus object in their circular orbit). When you balance the fan it ...

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The load increased but the input power driving the fan remained same. Moreover in very accurate measurements, the air drag can also not be neglected, all this will hold for a very another reason that the blades rotated by the motor are of very much comparable mass to the taped rubber & stuff.

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There are just two requirements, 1) correct frequency, and 2) sufficient amplitude. The correct frequency is, the resonant frequency of the glass cup (pane, cube, etc.). You will know you have sufficient amplitude, when the glass breaks! Both requirements will vary, depending on the material, shape, dimensions of the object, and other variables. If you ...

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Any structure that leads to a high Q system (the glass) will work and the trick is precisely matching the resonant (natural frequency ). By mounting the glass in a clamp that dissipates energy at a lesser rate than the sound energy that feeds it, the glass is doomed regardless of thickness or lack of imperfections. If the rate of energy input exceeds the ...

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Light frequency and wavelength are inversely proportional with a constant that is the speed of light (constant in vacuum). Both describe basically the same color within the spectrum, when light traverses a medium with a refractive index, its speed changes and affects the ratio of frequency to wavelength. What really matters is the energy carried by light as ...

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I will second what everyone has said... you will not like what you hear. At the most general level, sound is governed by wave equations, which are differential equations. Feel free to look the details up, I'm just looking to provide an overview. Energy is never created nor destroyed (in known physics). It just changes form. Your subwoofer has changed ...

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Would anyone want to help me on this journey? Probably but they all will probably give you the answer you don't want to hear. Which is that technology to prevent sound from affecting walls without any construction does not exist.

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First: what frequency should you hit? There are many, many different factors at play in determining the natural frequency of an object I know from experience. These are (not limited to): Thickness, density, elasticity modulus (you'll need two of those, e.g. Young's Modulus and Poisson Ratio), and of course shape. I'm not aware of any papers publishing a ...

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The blue shift is actually necessary to conserve energy. The photon has energy, and therefore has potential energy relative to the neutron star. It loses gravitational energy as it approaches the neutron star, and it gains energy in the form of blue shift. Indeed, to the first order in GR, the change in energy of a photon is equal to the change in ...

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I was just researching this kind of questions, since the derivation found in most textbooks, in terms of tension, seems a little unrelated to material properties. Three things: As pointed out, the tension T needs to be inside the square root The velocity of sound in the string material is unrelated to the (phase) velocity of the wave. As the formula shows, ...

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