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It's always possible to expand the potential in Taylor series around any local minima (in this example $U(x) $ has local minima at $x_0$ , thus $U'(x_0)=0 $ ) $$ U(x) \approx U(x_0)+\frac{1}{2}U''(x_0)(x-x_0)^2 $$ Setting $ U(x_0)=0 $ and $ x_0=0$ (for simplicity, the result don't depend on this) and equating to familiar simple harmonic oscillator ...


0

Resonant frequency of an object: A frequency at which the object will best capture and retain energy from a driving force. Driving energy into an object or system with a force at the natural frequency of the object will maximize energy transfer.


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The resonant, frequency is the frequency at which an object tends to vibrate. Every rigid object in existence has a natural structural resonance frequency, a frequency at which it, metaphorically speaking, wants to shake more than any other. If you vibrate an object at its resonant frequency, it will gradually shake more and more wildly. This frequency ...


3

Because so many different power generators are connected to the same mains circuit, it is extremely important that all generators maintain the same phase (and thus frequency) of the power supply. This makes the 50 Hz (or 60 Hz, depending on what continent you are on) a rather reliable reference signal. In this website the question of mains power stability ...


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As far as we know, light is mediated by a particle without rest mass. Special relativity says that such a massless particle's speed must always be observed to be $c$, irrespective of the observer's motion. In general relativity, a massless particle's speed as measured locally is also always $c$. No experiment so far has detected a measurable difference ...


1

In the equation: $$y(x,t)=Asin ~k(x-vt)$$ $A$ can be varied independently of $k$ and $v$ and hence of $f$. That is what is meant by saying that the amplitude doesn't depend on the frequency. Now, when you write the equation as: $$A = \frac{y(x,t)}{sin ~k(x-vt)}$$ it means that the ratio of the height of the string from the mean position at some point to ...


1

DC current is organized as following: positive potential applied to one end of the wire, negative potential applied to the other. Electrons move from one end to another with some speed. If you have one electron in vacuum and electric field from A to B, then there will be force acting upon that electron due to $F=eE$. Movement should happen along line ...


0

The relationship between wavelength and distance is similar to the relationship between frequency and duration, and no: neither pair is the same. You can see by using dimensional analysis. Wavelength is distance divided by cycles. Frequency is cycles divided by time. Multiply the two, the cycles cancel out, and you get distance divided by time, or velocity. ...


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Velocity is a more widely used term, usable for all moving objects and waves, while wavelength is of course only usable for waves. Wavelength is the minimal distance between two points of a wave with the same phase. Take for example a sinusoidal wave: the wavelength will be the difference between two maxima or two minima. The velocity of a wave is used ...


1

A wavelength is a particular distance, corresponding to the length travelled during a period, which is a special time. Since $v=d/t$ holds good for the distance $d$ travelled by a constant velocity object over any given time interval $t$, a fortiori this relationship holds for the special, particular time known as the period. So, yes, $v=d/t$ is how you ...


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The lambda is the distance between 2 points having the same phase like two successive crests the velocity is the wave can be conceived as how many crests for example passes through a reference in a given time you can use both equations but c=f*lambda is used if you have lambda , its proof is V = distance / time , if a crest traveled a distance = wavelength ...


2

CMB hasn't a frequency but a typical black body frequencies x radiances distribution. With the Planck law, the curve distribution gives the temperature of the radiation. I found this image in a previous question Relationship between temperature and wavelength? As you can see, each temperature has a typical curve. Yes, red/blueshift affect the ...


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No. Light travels at the speed of ... light, when measured locally in inertial reference frames. And the relationship between wavelength and frequency is $\lambda = c/f$. As the universe expands, the wavelength of the cosmic microwave background photons is "stretched" and thus their frequency must decrease by the same factor of $(1 + z)$, where $z$ is the ...


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Has the frequency of CMBR changed at all since the beginning of the universe? The usual answer is yes. It's thought to have redshifted by a factor of a thousand. But there is an issue: conservation of energy. Where did the energy go? This is an intriguing thread to pull, because we don't know of anything that's in breach of conservation of energy. There ...


0

Theoretically, the CMBR is what we see of the early visible universe. If we could be there to observe it, we might see much higher frequency radiation. However, due to the expansion of the universe, the wavelengths got stretched out and the frequency redshifted. Or perhaps you can say in our reference frame, we happen to measure these photons to be ...



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