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A rope is the best example. Think of a rope as a chain of particles attached to each other. You now grab the particle in the end and lift it up. Your hand applies the force that causes the acceleration of the particle. As that particle is starting to move up, it will pull the next particle beside it by exerting the same force as the hand applies. This ...


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An exponentially decaying tail is almost like having no tail for all practical reasons. For example consider the yukawa potential for interaction through exchange of a massive particle, it is $\propto e^{-\mu r}/r$ which is even a stronger tail than the asymptotic behavior of the hyperbolic secant. There we say that the interaction has the the effective ...


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First up thanks to all who took an interest especially @irishphysics who stuck with the question for some time. It turns out that the phenomena was analysed and solved by Lord Kelvin and is known as the Kelvin wave pattern. The pattern itself is the result of a spreading pressure wave which manifests itself as the curved diverging wave crests (the ones I ...


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The standing waves you introduced are models for how air moves as it resonates. In fact, each is called a mode (of oscillation). In the continuum approximation of air being an infinitely divisible, continuous fluid, you need infinitely many of them to simultaneously model arbitrary resonating movement. In practice, you can hope to neglect all but low ...


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The wavelength is fixed by the dimensional length of the tube, but since wavelength is equal to the speed of sound divided by the wave frequency, temperature will affect the frequency because temperature determines the speed of sound.


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There is no reason why you couldn't excite waves near a fixed surface, but these won't be surface waves. And if they are travelling close to a fixed surface, there'll be much larger material deformation than in surface waves, thus the attenuation will be strong.


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The answer to the first part of my question is on wiki, so I will not answer that here. After some research I have come up with the following answer to the second part of my questions. There are 4 types of waves we need to consider: Travelling waves (also known as progressive waves). (TW) Compound waves (CW) Stationary waves (SW) Infinite (harmonic) ...


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Under normal conditions, each photon can be thought of as a purely coherent entity with a definite polarization at all points in momentum (wavenumber) space. I discuss this notion in more depth in several other answers, notably this one here but the essential idea is this: lone photons propagate following Maxwell's equations (which are pretty much the Dirac ...


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The picture of the wave you are looking at is already polarized and that is plane polarized light. But this is not the general case, waves emitted by any one molecule may be linearly polarized but an ordinary light source contains large number of molecules with random orientations,so the emitted light is random mixture of waves linearly polarized in all ...


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The effects are twofold. The first is similar to the damage caused by an explosion. The shock wave will travel through tissue without too much harm until there is a density discontinuity, for example flesh to air in the lungs. You then get a "Newtons Cradle" effect which causes mechanical damage to the lungs. The second possible cause of damage is tissue ...


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Raphael, Active SONAR emits pressure waves that bounce off of things in the water; the timing of the pressure wave bounced back is used to measure distance and develop images of what is underwater. Given that the energy in the pressure wave dissipates at a rate defined by the inverse of the square of the distance traveled (1/r^2), it obviously takes a ...


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The energy is reflected from the cavity. In general, an optical cavity acts as a variable transmissivity mirror for a light source with very narrow linewidth (a laser). As you change the length, the cavity can go between highly transmissive and highly reflective. The specifics of how tranmissive and how reflective it can be depend on the reflectivity of ...


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Books generally teach sine or cosine waves because according to Fourier thereom any wave can be written as linear combination of sine or cosine waves. FOURIER THEOREM A mathematical theorem stating that a periodic function f(x) which is reasonably continuous may be expressed as the sum of a series of sine or cosine terms (called the Fourier series), each ...


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The sine function is just an idealized way to approximate wave motion, and indeed suitable for teaching the basic principles of how waves propagate, reflect and interfere with one another to create standing waves, but as with any real physical system, including the motion of waves, the closer you look the more you see non-ideal behavior. For surface waves ...


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Yes it is the (square root of) amplitude versus frequency. It presumably breaks the audio into short intervals and then DFT's each interval individually. The DFT of the entire sound would not be very insightful.


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Here's a minimum working example of a python program which generates a .wav file with a major triad of 440:550:660 Hz using sine waves. Your user input could be used to generate any frequencies for the chord. import math, wave, array duration = 1 # seconds freq1 = 440 # tonic (Hz) (frequency of the sine waves) freq2 = 550 # 2nd note freq3 = 660 # 3nd note ...


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From this link below " Refraction is the bending of waves because of varying water depths underneath. The part of a wave in shallow water moves slower than the part of a wave in deeper water. So when the depth under a wave crest varies along the crest, the wave bends. See "http://www.coastal.udel.edu/ngs/waves.html So my guess is its due ...


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The second approach is wrong. You cannot use the relation $E_{total} = h\dfrac{c}{\lambda}$ because this is equivalent to saying that $E_{total} = pc$ which is true only for massless particles. In this case it should be $E_{total} = \sqrt{p^2c^2+m_0^2c^4}$.


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In electronics, you are frequently more interested in the phase relationship between signals because that gives rise to the most interesting effects: when voltage and current are 90° out of phase, for example, there is no net power dissipation (purely imaginary impedance). When you look at a signal on the oscilloscope, you often tweak the time axis until ...


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By using the omega, you are plotting the x axis with a dimensionless quantity which makes it easier to interpret. By using time only, you are fixing the frequency of the sine wave so the plot does not have universal application.


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By adding the omega, you have the zero crossings at 0, pi, 2pi, etc. It is just a convenience to keep things oriented toward radians.


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The energy in the wave is distributed over larger and larger surface area as the spherical surface expands - unlike an ocean surface wave moving in only one dimension. I suppose in the spherical wave you could say there is a 'dissipation' over the surface. No losses in the wave, but rather distribution of the energy over larger area


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Internet fiber optic cables transmit via E-M waves in the light domain, instead of the radio domain. The frequency of the light is typically around 1500 - 1600 nm. A single fiber can also carry multiple frequencies (wavelength multiplexing). These different wavelengths are about 0.8 nm apart. Although some radio waves might be used in your downloads ...


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When you receive your radio-wave TV signal over the air using an antenna, the electro-magnetic wave is converted to electrical AC current that includes the same frequencies as the radio-wave. This antenna captures the radio (aka TV) electromagnetic wave via the Electric field strength part of the electromagnetic wave. The Antenna is connected to your TV ...


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The waves that carry signals for the internet are the same kind of waves used for radio and TV. It is also the same kind of wave as for visible light, x-rays, and gamma rays. The difference between these waves is frequency and wavelength. Radio and TV use waves longer, lower frequency waves than you can see. X-rays and gamma rays are shorter and higher ...


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I assume you're talking about the simple wave equation $$\ddot \phi=\phi'' \qquad (1) $$ To simplify things, let's talk about one dimensional waves. Everything still holds for higher dimensions, you just replace $\phi'$ by $\vec\nabla\phi$ everywhere. The energy density is $$u=\frac{1}{2}\left((\dot\phi)^2+(\phi')^2\right)\ .$$ Note that $u$ is the local ...


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Internet signals are mostly transported via cables. Some satellite links exist but they are less common. So we have cables and signals within them. Some cables are made of conducting metals others are glass fibers. The signals in the glass cables do not have the same properties as the ones in the metal wires, they are basically light that is sent through a ...


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The problem is that the dual slits are not infinitely narrow - the slit pattern is in fact the convolution of two infinitely narrow slits with a single wider slit. By the convolution theorem, the diffraction pattern, which is the Fourier Transform of the aperture function, is the product of the two Fourier transforms - so you see a series of equal intensity ...


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Let me use the complex numbers to make our lives easier: $$\Psi_1= \frac{A_1}{r_1} e^{i(\omega t - kr_1+\phi_1)}$$ $$\Psi_2= \frac{A_2}{r_2} e^{i(\omega t - kr_2+\phi_2)}$$ and thus the superposition of these waves is $$\Psi_1+\Psi_2= \frac{A_1}{r_1} e^{i(\omega t - kr_1+\phi_1)} + \frac{A_2}{r_2} e^{i(\omega t - kr_2+\phi_2)} $$ The square of the ...


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Wavelike properties usually means interference first of all. This is the first wavelike property of light that was demonstrated, I believe, and that's usually what you want. So, yes, matter can interfere with itself, as in the electron double-slit experiment. Often when people talk about matter behaving "wavelike" they're talking also about the fact that ...


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I don't think you are doing anything wrong. You're simply forgetting that your reflexion co-efficient, calculated as a phase, assumes sinusoidal excitation and thus, tacitly, you've assumed that the wave system is of infinite extent in time. In particular, the system has reached a steady state. What energy is going into the mass is periodically coming out ...


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There are multiple parts to your question. energy of a standing waves remains between the nodes When you look at the motion of a guitar string, it looks like this: The part between the nodes is moving, while the nodes remain stationary. When the string is flat (and moving fast) all the (kinetic) energy is indeed between the nodes. However, when the ...


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Energy transported by a standing wave gets thrown back by reflection. -> Consider a standing wave thrown back by total reflection - no energy transport takes place. A partly reflected wave sums up into a standing wave which gets overlapped by a running wave. In this case energy gets transported. If you want to understand why a guitar works, I would ...


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Let's think about sound waves. Sound waves is a pressure wave ie it propagates by the change of pressure in the air. If you have a standing wave then the places where there is high pressure and the places where there is low pressure remains the same. You can compare this fact with a swinging string fixed at both ends. The reason why this happens is that the ...


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Imagine,you have some balls and you are throwing the balls towards your friend and your friend is catching them. Suppose you throw 1 ball per second and then your friend will also receive 1 ball per second if you both are at rest with respect to each other. Now if you have some non zero relative velocity with respect to your friend then you will still ...


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It has nothing to do with physiology and everything to do with physics. If you were measuring the frequency with an entirely electro-mechanical system you would see the same effect. That was the whole point of Einstein's reasoning about light and relative motion that he used when developing the Special Theory of Relativity. The phrase "apparent frequency" is ...


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First of all, $\lambda$ is the wavelength and already carries a unit of length. So when you define $K=\frac{1m}{\lambda}$, this quantity would be dimensionless. And as you say, this really would be the number of cycles in one meter. But this is not the definition of wavenumber. The wavenumber and also the frequency are a measure of cycles in space/time per ...


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For linear deformations, when a material is compressed/stretched in one direction, it usually tends to expand/contract in the other two directions perpendicular to the direction of compression/stretching. This is called the Poisson effect, and the Poisson ratio is a measure of this effect. For some materials the Poisson ratio can be close to 0.5 (rubber) ...


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The article you refer to is talking about the speed of sound (or speed of longitudinal wave vibrations) within a material and how that relates to volumetric mass density. If you were transmitting sound from one end of a guitar string to another, this would be relevant. But the sound produced from a string is not related to the speed that it travels within ...


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The word "apparent" means "as observed at a particular point X". Different observers will observe different frequencies depending on their relative velocity to the source. This doesn't change the frequency of the sound that is generated; just the frequency of the sound that arrives at the ear of the observer.


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The characteristic speed, $S$ of transverse waves on a taut string or wire with tension $T$ and density per unit length, $\rho$ is $$S=\sqrt \frac T\rho$$ So indeed as you remove wire from play by wrapping it around the capstan, you decrease the wires density and increase tension. This increases velocity. and since $$\omega=\frac v\lambda$$ frequency ...


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Your intuition is right: the density of the string goes down a little bit when you increase the tension. HOWEVER: the wave in a string is a transverse wave which depends on the tension and the mass per unit length. If you double the tension the mass per unit length goes down by a small amount (the string gets a bit "thinner" because it gets longer) . Both ...


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The Doppler effect is a real physical effect that derives from the relative motion between a wave source and an observer. Say I'm driving along, playing a recording in my car of a steady F# tone. Since I am in the car traveling along with the speakers, I hear the tone as F#. My friend is standing on the curb with his boom box playing the same tone, and ...


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Think of a car stopped with it's siren or horn or radio (playing the same note) turned on, it has a certain fixed frequency. Then the car moves towards you, it's siren stays exactly at the same frequency as when it was stopped , but this frequency is apparently higher only to you. This is because more waves are entering your ear per second than when the ...


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Look at the equation. There are two components - one describes variation of the max amplitude with position (the $\sin (kx)$ part) and the other describes the variation with time ($\cos(\omega t)$). The antinodes must occur where the max amplitude is as big as possible (so where $|\sin(kx)|=1$). This will happen at multiple locations (there will be a ...


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It is theoretically predicted that superconducting layers might be able to act as reflectors through the so called Heisenberg-Coulomb effect. Out of these, you could of course form a cavity able to contain a gravitational wave in principle. This effect has, to my knowledge, not yet been experimentally tested, although several tests have been proposed, see, ...


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Taking the derivative of equation $y$ (as the hint states) and solving $x$ such that it is zero will give you your answer: $$ \frac{dy}{dx}=\frac{d}{dx}\left(2A\sin\left(kx\right)\cos\left(\omega t\right)\right)=0 $$


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The main question is how to contain the gravitational wave, and also how to make a cavity large enough to contain the gravitational wave. Also, reflecting the gravitational wave would be a big problem. So, all in all, no.


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"Non diffracting waves" are indeed possible, but there is always a practical limitation. The simplest example is the plane wave, which is an eigenmode of free space. It propagates by simply taking on the phase $\exp(i\,\vec{k}\cdot\vec{r})$. The practical limitation is of course that it has infinitely wide extent. Practically, diffraction is always present ...


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Maybe what they mean by same profile is the general shape of the function f(x). For example in a gaussian beam waist, the transverse profile is the gaussian function as the one you have mentioned, but the spread of the beam increases along the propagation axis . To sum up, the shape of the transverse profile is always a gaussian, but with a spread that ...



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