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1

You simply need to define a few state variables. Here is the standard, control theory recipe that should get you going: Let $x_1(t) = x(t)$ and $x_2(t) = \dot{x_1}(t)$. Then your vibrating string equation becomes $M \mathrm{d}_t x_2(t) + C x_2(t) + K x_1(t) = b(t)$. That is: $$\frac{\mathrm{d}}{\mathrm{d}\,t} ...


1

The answer depends on lots of factors: The nature of the speed bump, The nature of your vehicle's suspension, The weather (your suspension is a bit stiffer in winter than summer), Whether there's stuff such as a rather low oil pan under your vehicle that you would rather not lose to your vehicle bottoming out, and Which you care more about: The impact on ...


5

Normally, suspension consists of a damping component and a spring component. For such a suspension, higher speed means higher acceleration and greater force. Driving faster will cause a bigger jolt. However, high end cars these days use active suspension - and that changes everything. With active suspension, you can either respond quickly to bumps in the ...


5

Put more simply: sound waves are attenuated as they propagate through air (this is more easily measured for very short wavelengths, e.g. ultrasound). This means they lose energy - which is turned into heat of the air. The amount of heating, however, is very very small. Let's do the math. A sound wave of 120 dB (really loud) has energy of only $1 ...


1

A qualitative picture of what happens in a gas can be made in terms of whether the behavior is random or non-random, oscillatory or steady. Temperature describes the random motions of the particles that comprise some object. Correlations, if they exist, disappear rapidly with distance between particles. In an ideal gas, correlations don't exist, period. ...


7

Sound waves do generate changes in temperature because the propagation of sound is an approximately isentropic process. Keep in mind though that changes in static temperature can very well occur without the generation of heat. Moreover, the pressure changes associated with sound waves are of such a small magnitude that the observable temperature changes are ...


3

Heat corresponds to random movements of atoms and molecules. It travels only through conduction - slowly. Sound consists of ordered movements, travelling through a medium as a wave (although it can also stand still, as in a standing wave). Large numbers of atoms or molecules move back and forth in synchrony. Sound eventually becomes random, as it is ...


1

There's not much difference. Thermal vibrations would be perceived as sound (noise) if they were intense enough, but they are not. The thermal vibration amplitudes at room temperature are small enough that the ear is not sensitive to them. I've been told that the sound pressure level for thermal vibrations is close to, but below, the threshold of ...


3

A plank is a complicated example to choose because it's a composite material with a complicated structure. A better choice would be a piece of iron or some other homogeneous material. In that case the speed of sound is given by: $$ v = \sqrt{\frac{K + \tfrac{4}{3}G}{\rho}} $$ where $K$ is the bulk modulus and $G$ is the shear modulus. The bulk modulus is ...


2

I guess you mean to ask - is the amplitude of the vibration proportional to the speed of the sound waves it produces? The speed of sound in an ideal gas for relatively small amplitudes ($\frac{\Delta P}{P} \ll 1$) is $v=\sqrt{\frac{\gamma P}{\rho}}$ where $\gamma$ is the adiabatic constant (i.e. $PV^\gamma=const$), P is the average pressure, and $\rho$ is ...


0

Volume is not strict word for describing sound (look, how many meanings in acoustics it has) http://en.wikipedia.org/wiki/Volume_%28disambiguation%29 "Loud" sounds are basically those of big amplitude. And amplitude of wave and its speed are two different things that have not much in common. Hitting a plank harder will make louder sound (the plank will ...


0

In the context of this specific video, I believe that you cannot truly have a perfect square plate no matter how good your tools are. Therefore the pattern actually does settle on a specific frequency and not at two different frequencies.



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