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So the length of a wave is the distance between two compressed regions as shown in this representation of a longitudinal wave: is in general not true but rather it is a pictorial representation for simple cases in one dimension. A wave is any solution of a wave equation of the form $\Box \psi(\textbf{x},t) = 0$ that can be expressed in the form $$ ...


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You don't need a particular point on the wave. You only have to make sure it's the same point on each successive wave. If you have a microphone, hooked to an oscilloscope, you can measure the time between peaks (or troughs, or zero-crossings), multiply by the speed of sound, and that's your wavelength.


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In those notes, it states that the left part of the string pulls the dot with a force proportional to the slope. However, the right side pulls the dot in the other direction with a force proportional to the slope, so that if the slope is constant, there is no net force on the dot. The only way to get a net force is for the slopes to be different on the left ...


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The wavelength is not defined as the length after which the waves repeats itself: that is only a pictorial representation that works in one dimension for simple one component waves but it is not valid in general. Instead, given any solution of a wave equation represented as Fourier transform $$ \psi(\textbf{x},t)=\int ...


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Suppose you shine a linearly polarized laser at the wall. Let's call the direction of laser propogation $\hat{z}$ and the direction of the electric field polarization $\hat{x}$. Then if you plot the $x$-component of the electric field vs. $z$, you will get a sine wave. The wavelength of the light is the wave length of the sine wave. So if one peak was at ...


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The standard procedure is the following: starting from $ \langle nlm|\,\partial^2_z\,| n'l'm'\rangle $ insert the identity operator with respect to the position basis $$ 1 = \int d\textbf{r} |\textbf{r}\rangle\otimes\langle \textbf{r}| $$ to have $$ \int d\textbf{r}\, \langle nlm\, |\,\partial^2_z\,|\textbf{r}\rangle\cdot\langle \textbf{r}|n'l'm'\rangle. ...


1

Yes, I think your description is pretty reasonable. Suppose you represent your medium as made up of lots of thin strips: Energy is transfered along the medium as one strip rubs against another: This diagram is supposed to show friction (the red line) pulling the right strip upwards as the left strip moves up - possibly not one of my more effective ...


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The vibration of the particles isn't only up and down. In the other question Wendy Krieger said ocean waves are transverse waves. Take a look at the Wikipedia Wind wave article where you can see this gif: GNUFDL image by Kraaiennest, see Wikipedia See the red test particles? They don't just go up and down, they go round and round. They have an angular ...


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The question is begging a simple answer: Because nature can be represented as resonators that respond in a delayed way we adopt to study it using complex numbers. When an electronic circuit is excited by a regular periodic source of tension (measured as a real function - $V_0\cos(\omega\cdot\ t)$ for instance) the most common answer is a variation in the ...


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No. A sonic boom is an acoustic disturbance caused by supersonic flow over an aircraft's surface. Supersonic flow creates a discontinuous shock boundary that emanates from the aircraft surface and the shock wave propagates behind the aircraft with a large amount of energy, however dispersive as it travels through the atmosphere. Resonance does require an ...


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If we look at the sonic boom as a $\delta$-function, where we have a really loud sound for a really short time, then it will be able to excite all frequencies at the same way. You can actually compute this by showing that $$ \delta(t)=\frac{1}{2\pi}\sum_n e^{int},$$ which show how the $\delta$-function is actually composed of all frequencies. Then it's ...


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Recall that $cos\alpha\cdot sin\beta +cos\beta\cdot sin\alpha = cos(\alpha+\beta)$. If you suppose that $B_1=B_0\cdot sin\phi$ and $B_2=B_0\cdot cos\phi$, it turns out that: $B_1cos(kr-\omega t)+B_2cos\phi=B_0\cdot sin\phi \cdot cos(kr-\omega t)+B_0\cdot sin(kr-\omega t)\cdot cos\phi=$ $=B_0\cdot cos(kr-\omega t+\phi)$.


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How can I get from what is given to the direction of $\vec{k}$ The E-field has only a y component. And the B-field has only a z-component. Since this is a plane wave, then you know that the direction of propagation must be in either positive or negative x. From the information given, I believe it's actually ambiguous which direction the wave is ...


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What is the explanation for this phenomena? "Water Hammer" https://en.wikipedia.org/wiki/Water_hammer There is a study from "Hasson and Peck", 1964, which explains "Thickness distribution in a sheet formed by impinging jets." It's all basically Bernoulli's equation; "Velocity -> pressure -> velocity" and then simply continuity. Anouther good source is the ...


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As I understand it the derivation of the function $\sin(\theta)$ of angle $\theta$ comes from the triangle. This is purely mathematical. The equation that you quote $$y = A \sin(wt + \theta)$$ can be derived by solving the second order differential equation for simple harmonic motion $$ {d^2x \over dt^2} = -{k\over m} x $$ here for a mass, $m$, on a ...


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"Sound energy" must mean the vibration of the air (or other medium in contact with your eardrum). If water molecules collide with each other and with air, then there is a transfer of vibrational kinetic energy. Vibrations in air propagate to your ear as a pressure wave. For your second question, the more disturbance of the water flow and the more ...


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I think this originated with Hadamard and his Method of Descent. See Lectures on Cauchys Problem in Linear Partial differential Equations--starting on page 7. His results were that waves in two dimensions did not propagate sharply, but had a wake (a tail, ..). Eg. a circular wave propagating in two dimensional space vs. a spherical wave propagating in three ...


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No. The particles of the medium in which the wave is travelling (assuming that this is a mechanical wave) aren't actually displaced in the direction of the wave, but are merely disturbed. In the case of a longitudinal wave (e.g. sound), a particle will for a time be moving in the direction of propagation the wave, for a time be at rest and for a time be ...


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A graph should clarify the relationship between two quantities, requiring the least amount of mental effort on the part of your audience. If you are trying to show the change of density as a function of position along a wave, you should plot position along one axis, and density along the other. Whether you use vertical deflection as a measure of density or ...


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Can electrons reflect light? Yes. Like CuriosuOne said, electrons are shiny. I kid ye not, google on electrons shiny. Metals are shiny because they have free electrons. Check out this question about the colour of metals, where Ali said a metal is are silvery because it "reflects all wavelengths specularly (more or less)". Also see this article by William ...


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Think about what the wave vector represents, and what kind of wave your equation describes. The most general equation for the spatial variation of the electric field for a plane wave is $$\mathbf{E}(\mathbf{r}) = \mathbf{E_{0}} e^{-i\mathbf{k} \bullet \mathbf{r}}$$ where $\mathbf{E_{0}}$ is some vector with no dependence on $\mathbf{r}$. This can be ...


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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 ...


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As stated in previous answer,many things happen in water ripples.But a major reason for increment in wavelength is loss of energy as the wave progresses due to non ideal conditions.Since wavelength is inversely proportional to energy of wave,as energy decreases,wavelength increases.Hope this helps :-)


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Electromagnetic waves are only an observed phenomenon. There is no travel. As an example we can choose a photon which is "traveling" from Sun to Earth (for simplicity we do not care about gravity issues here). That means that Sun is emitting a bit of energy (a momentum) which is received by Earth. So far everything is OK. But what is happening between ...


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Since, electro magnetic waves have electric and magnetic vector. Due to this EM waves show electric and magnetic field. An electric and magnetic field have no need a medium to show thier effect. Hence in the presence of electric and magnetic field vector which vibrate perpendeculer to each other and get pertervation EM waves travels in vacuum.


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Several things happen with ripples. First - they are comprised of different wavelengths. That may be hard to explain in plain English, but basically the only way that a wave can have a single wavelength is when it goes on for all infinity. A short "wave packet" must contain different wavelengths. Next - the speed of propagation of these different ...


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If we assume that you're talking about a broad sound wave traveling through a large, homogenous medium (air, water, rock) then normally, no: the pressure waves that are sound involve only motion along the direction of the sound's travel. You can wonder if the higher-pressure zones would tend to push the particles of the medium sideways, but remember that ...


3

That video is very poor in one aspect: particles in the sound field doesn't move "horizontally" nor "vertically". Really, the proper word is "longitudinal motion" and you are in fact asking about "transversal motion". In basic description, the air is considered to be an ideal fluid. Therefore no shear stress is possible and hence no transversal motion as ...


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If you have any kind of solid material, it will become a little bit thicker as you compress it, and thinner as your stretch it. This means that a "one dimensional" wave traveling longitudinally down a rod will in fact cause some lateral motion. The ratio of displacements in the perpendicular direction is obtained from the strain (relative displacement of ...


1

No, quantum/particle theory came later. What Einstein realized was that, travelling at the same speed as a light wave, the forward component of the fields "freeze", leaving only the lateral components able to vary. So the interplay between electric and magnetic fields which characterize electromagnetic radiation would be grossly affected. All of this takes ...


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The situation you are describing is an example of Fresnel diffraction (or near-field diffraction). In general, when a wave propagates every point of the wave front can be thought of as its own source of waves traveling in all directions (called Huygens construction). It turns out that neighboring point sources along an infinite straight wave front reinforce ...


1

You will benefit by finding some tutorials on wave theory. In brief, assuming a spherical wavefront from the emitter, you are correct there's no direct path to the receiver. However, the edge of yourabsorber there causes diffraction (Huygen's principle), so thatsome of the sound wave (energy) will make its way to the receiver. You can see a demo of this, ...


0

In general, if no further information is given, you can assume that the focal length is approximately correct for the visible spectrum. Note that, in your example, since the focal length is specified as 25 mm, as long as the FL is within 0.5 mm of 25 mm the lens is within spec. Even with window glass, you should be able to get this performance from 400 nm to ...


1

Classically EM radiation is just a wave (not a particle) and the double slit experiment is only the result of the well known interference proprieties of waves.In quantum mechanics we've got the wave-particle duality, and so the light could be seen as composed by particles, photons. So the first thing to point out is that mixing the two approaches (talking of ...


0

"How exactly the RADAR works? Is it possible for RADAR to work with 1940s clocks?" is, of course, two questions, and the second is easier to answer: in the sense that we talk about it today, where a signal is analyzed and a digital readout provides timing information, 1940's radar did not do that at all, and therefore did not "work with clocks" at all. The ...


0

One does not need a precise clock for radar because the time that a radar system is measuring is very short, on the order of a few microseconds to maybe a millisecond (that's already 300km of distance!). The long term stability of the timing system is therefor irrelevant, but it's long term stability that makes precise clocks hard to build. In terms of ...


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I think this question is more about the engineering (and economics) of manufacturing microwave ovens. The standing wave pattern can create hot and cool spots in larger food items that are not moving inside the oven. The rotating plate is sufficient to move the food around so that most of the food is not stuck in a node that creates large temperature ...


3

You need to keep well in mind that the sensation of color is a semantic meaning that the human mind's processing attaches to the spectral content of light. The mixing of "primary colors" was experimentally found (first by artists for red, yellow and blue with natural pigments, then later for, usually, red, green and blue by photography and color projection ...


3

Yes - Thixotrophic fluids can change their rheological properties (viscosity) as they are stressed by motion. And this can change natural frequency if the fluid is contained within a waveguide (resonant cavity).


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John and Rod already pointed out that the expected frequency shift from driving a car is "small"; I would like to expand a little more on the way FM works. FM = Frequency Modulation. The carrier (nominal center frequency) is being modulated - that is, in order to convey the audio content, the frequency is actually moving around deliberately in order to get ...


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To further add to John Rennie's answer: you don't even need autotuning for a frequency drift of the magnitude John calculates (10Hz): all FM receivers I've ever dealt with (I qualified as an electrical engineer in 1985 and worked a few short years in communications before returning to study) demodulated with a phase locked loop detector, whose job it is to ...


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It does! However it doesn't change the frequency enough to matter. An FM transmission is not a precise frequency. Instead it spans a range of about 100 or 200kHz depending on which country you are in. So your FM radio actually accepts a range of frequencies either side of the central frequency. Let's suppose you're travelling at the maximum speed permitted ...


2

Basically Huygens Principle is just a way that was envisioned in the 17th century to describe how wave behaves and is understood as in the following picture. Each point on the wavefront radiates spherical waves which interfere to preserve it during propagation. This picture is inspired from Rayleigh Scattering where the emitters are actually all the ...


0

I don't know the idea in detail, but broadly speaking you take some points on the your wave, draw spherical wave maxima around the points, and then find where there is constructive interference. This will give you a set of new points that basically describe where the wave front ends up. Of course, in nature this is supposed to happen for each of the ...



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