# Tag Info

1

Nice question and lovely piece of optimization! I have been thinking about that for a while. I can only answer from a point of physical music acoustics. It appears to be interesting feature for drum design and construction but my considerations end with a conclusion that it is not much useful in praxis. Here is why: Case 1 - Directly struck drum: the sound ...

2

You typically have one position and one velocity variable per oscillator. The equation of motion of mass $i$ is $m_ix_i''=k_ix_i+$coupling terms. If the forces from the coupling terms are small, the frequencies do not change much. If the coupling is large, you will have as many modes as oscillators, but the frequencies can be anything. You wind up finding ...

0

Here's my addition. Many of the answers above use the erroneous argument that frequency is the determining quantity, on the basis that the same object viewed in different media appears to be the same colour. This is meaningless, since the light has to travel through the vitreous humor (with refractive index 1.33) immediately prior to reaching the retina. ...

2

Building on prior answers, the facts are: Color is determined by the energy of the EM Wave that reaches your eyeball. Energy is defined as $E = hf$, where $h$ is Planck's constant and $f$ is the light's frequency. Thus, the color of an EM Wave is defined by its frequency. In other words, measuring the frequency of an EM Wave is sufficient to identifying the ...

0

In the general case the frequency of a wave and its kinetic energy are not related. As you can derive from Energizer 777's answer one can increase the frequency and this time decrease the amplitude of the wave generator and you approximately need the same amount of energy to support the damping of the wave from dissipation processes. The point is that an ...

2

Good theoretical answer is that it results from linear acoustical wave equation and its presuppositions. It is therefore good approximation whenever linear acoustics still can describe the wave propagation (that would by e.g. 90% of room acoustics practical examples). Typical examples of problematic models are large-amplitude events (e.g. a shockwave after ...

1

The spectrum of various resonant tube arrangements (half-open, fully-open fully closed) is something that can be measured in a very basic laboratory and gives solid evidence that the claim is true over the kinds of frequencies that are accessible in such a lab. Say a few hundred to a few thousand hertz.

3

It's a bit pat maybe, but if the wavelength-dependence were detectable over human distance scales, the (quality of) sound (not just the volume) of music, speech etc. would depend noticeably on how far one were from the source.

0

The frequency of a standing wave on a guitar string is given by $$f = \frac{v}{2L}$$ where $v$ is the velocity, and $L$ is the length of the string. It can be shown by using the wave equation (which I'll skip, as it is a more complex derivation) that the velocity of a wave on a string is related to the tension in the string and the mass per unit length, ...

-1

Frequency of anything is infinitely variable up to the point of fusion. And then again Infinitely variable to to the next densest element order of matter. frequency of anything cannot be truly calculated as gravitational forces from its most central particle outward lowers in destiny Infinitely as well from one state of matter to the next. The best one can ...

3

Consider an arbitrary potential energy $V(x)$; take $x_0$ to be an equilibrium point, that is, $V'(x_0)=0$. Next, Taylor expand $V(x)$ for $x$ close to $x_0$: $$V(x)\approx V(x_0)+(x-x_0)V'(x_0)+\frac{1}{2}(x-x_0)^2 V''(x_0)$$ The first term is just a constant (ie, irrelevant for energies), and the second one is, by definition, null; therefore we find ...

0

The color of an object is completely determined by the refractive index and the geometry of the object. The reason why it is not obvious is that one has to takes the imaginary part of the refractive index into account. The real part determines the wavelength of light in matter and the imaginary part describes absorption of light in matter. When you ask what ...

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