New answers tagged

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In your example, a wavelength and a wavenumber represent in a different way the same information as there is a direct conversion between the two quantities. You can use the same reasoning to answer your question about the m/s and s/m: You have a speed $v$. Let's define a new quantity based on that speed, $$\rho = \frac{1}{v}$$ which we conveniently call ...


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Let us imagine that the disturbance that causes the wave is located at position x=0. If the disturbance is oscillatory then it could be of the form $\displaystyle y(x=0,t)=A\sin\omega t$, in which y denotes the displacement of the particle of the medium, $\omega$ is the angular frequency of oscillation. The quantity $\displaystyle\omega t$ is called the ...


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A wave propagates through the medium due to the interacting particles in the medium. The medium is nothing but a certain region of space containing some interacting particles. If there are only identical particles, the the medium is homogeneous. Otherwise it is heterogeneous. A wave in such a medium is nothing but a disturbance in a particle's energy in that ...


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Remember that noise is unwanted frequency signal superimposed into the original frequency. This means to reduce noise, you need to block the unnecessary frequency components. The effect of noise increases while increasing the amplitude because amplitude is a measure of loudness. So the amplitude (loudness) of the noise also increase as you increase the ...


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This is a common misconception about what boundary conditions do and how they do it (for example here). You discussed two types of boundary conditions, Neumann and Dirichlet. In Neumann boundary conditions, we impose that the derivative of the variable normal to the boundary is specified, generally to be zero. With Dirichlet, we impose the value that the ...


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When deriving the wave equation we assume the horizontal component of the tension in the string is constant and equal to $T$ (the tension when the string is at rest). To calculate the tension in the string let's start with the wave then zoom in to a small segment of it. If we take a segment small enough that we can consider it as a straight line, then the ...


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The tension of the string is a constant, if there is no vibration on the string. A wave is produced on the string when you give an unbalanced force on the string which varies the original tension of the string. The velocity of the wave now depends on the value of the tension. The given equation is valid only for small amplitude vibrations. The tension is ...


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The following interpretations are taken from Thorne [2014]. Chapter 17, entitled Miller's Planet, discusses the issue of the large waves on the water planet in the movie Interstellar. There Kip mentions that the waves are due to tidal bore waves with height of ~1.2 km. In the appendix entitled Some Technical Notes, Kip estimates the density of Miller's ...


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Do u really think that velocity is constant?i think in this equation nothing is constant.if tension increases per unit mass decreases and it may make change in velocity or not if the ratio remains the same.further tension depends on some variables such as intermolecular force,elasticity etc


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Suppose an x-axis which points to the right. A wave produced by a source travels to the right. The displacement due to the wave at position $x$ at a time $t$ is $y = f(kx \pm \omega t)$ where $f(kx \pm \omega t)$ is a function which satisfies the wave equation. It might help your visualisation if you think of that displacement corresponding to a peak. ...


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The points at which the sine is maximum will satisfy $kx+\omega t = \frac{1}{2}\pi + 2\pi n$ with $n$ an arbitrary integer. So at a given time $t_1$ these peaks are at $x_n (t_1) = \frac{1}{k}(\frac{1}{2}\pi + 2\pi n - \omega t_1)$. Now look at these peaks a short time $t_2 = t_1 + \Delta t$ later. You will easily find \begin{equation} x_n (t_2) = ...


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Let's take the argument of the function i.e, $kx-\omega t$. The argument of the function should remain constant,(equivalently the phase must remain constant)for a particular section of the wave. \begin{equation} kx-\omega t=\lambda \end{equation} where $\lambda$ is a constant. Differentiating both sides we get, \begin{equation} k\frac{dx}{dt}=\omega ...


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In your layout, imagine the "antenna/you"-capacitor being parallel to the existing one, the antenna being the upper plate. Parallel capacitors add up their capacity. So how do you become the plate although you are not connected to the wires? The first step is to understand is that this setup (inductor + capacitor) will generate frequencies, as you could ...


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The player's hand acts as a grounded plate remembering that the player is a reasonable electrical conductor. The capacitor is part of an inductor-capacitor circuit, as you have shown above, which control the frequency of an oscillator. So what is missing is a clear indication that the bottom part of the circuit is connected to the earth/ground.


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A wave has the property of periodical energy transfer without matter transportation. For clarification. A falling into water stone makes the water oscillating up and down. Due to dissipative processes a pure up and down oscillation instantaneous over goes to a moving away from the impact point in all direction up and down oscillation. On the boundary ...


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Wave velocity, when not otherwise specified, usually means the phase velocity: the rate at which the phase travels in space. This site animates the differences between phase and group velocities. The group velocity is the speed at which energy is transported. So if the context implies that the wave is carrying energy, the wave velocity is also the group ...


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In a strict, linear view of the world, waves simply transfer energy through space or media. But the world is almost never linear, and if one looks closer mass will be set in motion or transported with the wave energy. Examples? Ocean surface waves. Although energy is transported across the surface, one can trace local elliptical transport of water molecules. ...


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One must distinguish the underlying quantum mechanical framework from the emergent classical mechanics and electrodynamics framework when discussing waves. In classical mechanics wave equations are solutions of differential equations which depend on the $(x,y,z,t)$ variables of massive ideal particles which are derivable from differential equations . These ...


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The waves, the particles are associated with, are purely of mathematical construct. The wave or more formally the wavefunction assigns probability amplitude at each spatial coordinate at a specific time; the square of which gives the probability of finding the particle at that coordinate at that specific time. These waves don't transport energy, charge or ...


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Most simple waves that you've studied probably obey the wave equation: https://en.wikipedia.org/wiki/Wave_equation#Scalar_wave_equation_in_one_space_dimension. This equation describes many kinds of commonly-encountered waves quite well: e.g. vibrating guitar strings, water ripples, sound waves through air, light traveling though empty space. These kinds of ...


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Trust the math. The first equation gives a specific speed of the wave. Second equation gives a relation between speed, frequency and wavelength. You don't get much information out of 2nd equation however the 1st equation explicitly states that the velocity depends upon the medium. Just take sound for example, if the speed were dependent on frequency the time ...


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Those two equations tell you 1) The speed of a wave on a string depends on only tension and density of the medium, not the frequency of the source. 2) IF the frequency of the source if $f$, you can find the wavelength by $\lambda = v/f$. High frequency sources produce shorter wavelengths, and vice versa. You're NOT free to choose both the wavelength and ...


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You are not changing anything other than writing the spring constant for one spring in another way. You are still considering the same three particles you started with. The sequence is as follows. One spring of spring constant $k$ is in series with $N-1$ other springs. So the spring constant of the $N$ springs $K= \frac k N$. This comes about because if ...


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This demonstration using the Ruben's tube set-up might help. I always found this to be one of the most exciting visual demonstrations of sound waves.


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I you have a small speaker then you could lay it down and put a small piece of paper on it.Although not visible to the naked eye, when the speaker is switched on , a small piece of paper placed on the speakers will serve a good way to visualize the movements of air particles. Also to give an idea of the intensity of sound waves the speakers can be brought ...


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Sound waves can be visualised, but I can not imagine how it could be made without special equipment. You can find many related photographs on the internet if you search for the "Schlieren photography".


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Regarding the second option , The waves can't produce interference since they're in phase.I they weren't (eg. if they had a phase difference of pi) they would cancel out on superposing however since the coefficient of the kx term is zero , they're in phase. I've answered the question assuming you are familiar with the basics , however ,if you need more ...


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In case of a travelling observer , there is change in wavelength,and the magnitude and sign of change in wavelength depends on the velocity of the observer. Let's say an observer moves towards a stationary source emitting pulses with a frequency of 'f' with a velocity vo . A pulse reaches the observer and by the next time a pulse reaches the observer, the ...


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From considering the De Broglie Wavelength, $h/mv$, we can show that every wave has momentum if it is considered as a particle derived by its Wavelength.


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Mechanical waves are those that need a specific medium for their propagation. Of course, the medium has to be physical. There are two types of mechanical waves: transverse and longitudinal. But, first of all, electromagnetic waves that show transverse property are not mechanical waves since they don't essentially need any medium for their propagation. The ...


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In the case of beat, you're interested in how a pair of waves will 'sound' for a particular observer at some point $x$. So for both waves, $kx$ is a constant and can be ignored.


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The speed of sound in a perfect gas does not depend on frequency. In real gases, however, the speed of sound depends (slightly) upon frequency, this is called dispersion (have a look at Is speed of sound really constant?). As well, the speed of sound being constant depends on small displacements.


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This is about Froude-number. It's already stated behind the link of Answer of Duncan Harris; The concept of hull speed is not used in modern naval architecture, where considerations of speed-length ratio or Froude number are considered more helpful. Your questions; 1) Why this phenomenon occurs when the wavelength of the wave and the length of ...


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Take your expression: $$ v=\frac{\omega}{k} \tag{1} $$ We'll write $\omega=2\pi f$, rather than $\omega = 2\pi/\tau$, where $f$ is the frequency of the wave and substitute for $\omega$ and $k$ in equation (1) to get: $$ v = f\lambda \tag{2} $$ The wavelength $\lambda$ is the distance the wave moves in one cycle, and the frequency is the number of cycles ...


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Huygens worked with scalar, longitudinal waves. This was proved to be incorrect in 1821 by Fresnel, who showed that polarization requires transverse waves. A (relevant but incomplete) history of light and how well different models explain certain experiments is given in my recent lecture ''Classical models for quantum light''; see ...


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In general, the speed of sound in gas depends on composition, temperature and pressure. If those three are constant the speed of sound is constant.


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There is an addition needed here. The speed of a wave is constant through a homogeneous isotropic medium. Sound wave is a mechanical wave which propagates as compression and rarefaction through the medium. It actually pressurizes and depressurizes certain region of medium. The medium has several properties upon which the velocity of sound relies up on. If ...


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This wikipedia article is written like the perfect answer to your question: https://en.wikipedia.org/wiki/Hull_speed The answers it provides are: Question 1: When the wavelength of the bow wave is equal to the length of the ship, the bow wave interferes constructively with the stern wave, causing taller waves in the wake and thus more energy radiated in ...


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No. It is an equation of a moving function. Take any general function dependent on position and time such that the function is f(x+ct). Now, partially differentiate it by applying chain rule. You will see that you end up with the same differential equation as above.


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Solutions to the wave equation need not be periodic. In fact, any profile with the argument $x \pm c t$ will satisfy the wave equation.


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In short, yes, it will be louder. In the simplest case, if you were able to duplicate the exact signal everywhere in space, you would actually get 4 times the intensity - sound waves add linearly, but intensity adds quadratically. For two uncorrelated sources (if you played different white noise signals through each speaker) you would only get a factor ...


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Intuitively if you have some flexible medium and you "strike" it with a pulse, the parts that have less tension will move more freely than the parts that have stronger tension. However if this medium is "stretchy" then the more it is displaced the stronger it tries to go back, possibly overshooting, causing oscillations. If there's some resistance to make ...


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You pull a small piece of a rope up, and as that piece goes up it pulls the piece adjacent to it up and as that piece goes up... When you move your hand back to it's original position you're applying a force to the piece again and it pulls the adjacent piece down, etc... Model of displacement as a function of position and time: $y(x,t) = y_{max} ...


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Your casual observation is astute; there is a relationship between the coils of a spring and sinusoids: $$e^{ix} = \cos x + i \sin x $$


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A typical wound-into-a-cylinder spring is a helical in shape. And yes that means that subjected to tension and viewed from the side the transverse displacement will be sinusoidal to the same precision with which it approximates a helix.


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Phase difference is nothing but average wave number multiplied by path difference $\dfrac{2\pi x}{\lambda}$ where $x$ is distance between two particles $x$ can further be written as: velocity $\times$ time That is Phase difference $= 2 \pi v t/\lambda = 2\pi n t$ Where $n$ is frequency


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Seventeen months later, I found the answer. What I described in the question is called choked flow. It means that, in the choke, fluid speed must be supersonic in order to "cut" disturbances coming from downstream. Ergo, fluid speed doesn't need to be supersonic in the entire pipeline. Also, it is achieved only for pure gas or multiphase (oil + gas) flow, ...


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For a general answer concerning these types of systems, we can take the simple gravity pendulum as a representative example. The equation of motion is generally non-linear, but can be approximated to be linear at small angles (small amplitudes). See also the small angle approximation section in the linked wikipedia article. For progressive waves you will ...


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tl;dr: It's because of discontinuous change in impedance $\rm Z.$ Reflection Coefficient $\rm R$: Let the point where two media meet be $z=0\;.$ At $z= 0\,,$ the incident wave is given as $$\psi_\textrm{inc}(0,t)= A\cos\omega t\;.$$ The total force exerted by the input terminal of the second medium is given by $$\begin{align}F&= ...


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Energy of a wave is an oscillating quantity. Higher the frequency of the wave the more difficult it becomes to measure the energy instantaneously. Imagine sending an alternating current through a direct current ammeter. The ammeter wouldn't know how to respond. But if the same current is sent to an ac ammeter it reads the root mean square value of the ...



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