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2 votes

Why do we hear frequencies in the basis of sine waves?

To put your question in a wider perspective: consider white noise As we know: the expression 'white noise' is used for continuous sound that consists of random frequencies; random shifting of ...
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7 votes

Why do we hear frequencies in the basis of sine waves?

The human sensory system is a large ensemble of detectors which are made of nerve cells. A complex sensation occurs when a stimulus triggers a large number of nerve cells, while a simple sensation ...
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18 votes

Why do we hear frequencies in the basis of sine waves?

The "reason" that the Fourier decomposition is the "correct" one has to do with the fact that both signal detectors (microphones, ears, etc.) operate as driven harmonic oscillators....
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3 votes

Why do we hear frequencies in the basis of sine waves?

We can and do in some cases. Take a look at the Zernike Polynomials for decomposing 2-dimensional frequency distributions, for example. The short answer is that sine waves are nice and clean, behave ...
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3 votes

Is wavelenth of a particle relative according to Wave Particle Duality?

This is indeed counter intuitive, but then again quantities like kinetic energy also aren't conserved when you transform frames. For a consistent treatment you can have a look at the Klein-Gordon ...
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4 votes
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Is wavelenth of a particle relative according to Wave Particle Duality?

The de Broglie relation is a forerunner of the quantum mechanical wave equations. We now know that the wavelength in the wave particle duality is not a wavelength in space. It is the wavelength of the ...
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1 vote

Does the "particle in a box" necessarily form a standing wave?

No. Any "suitably well-behaved" function $\psi_x$ can be the wave function of the particle in a box (infinite well version) provided that it is zero both at and outside the walls of the box. ...
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0 votes

What is the potential energy of electromagnetic waves traveling in air?

Potential energy is not an intrinsic quantity of any physical object, and therefore it is not meaningful to ask of the potential energy of an electromagnetic wave. In some sense, you can view the EM ...
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1 vote
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How to distinguish between zeroth, second and higher order sounds?

All these modes are oscillations in the conserved densities (particle number, energy, momentum, etc.) of an interacting many-body system in approximate thermal equilibrium. Consider first ordinary (...
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4 votes

Does the "particle in a box" necessarily form a standing wave?

It is completely possible for a particle in a box not to be in a standing wave state. In fact there are infinitely many more non-standing wave solutions to the particle in the box than there are ...
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5 votes

Does the "particle in a box" necessarily form a standing wave?

It’s important to make a distinction between two different “particle in a box” setups. 1.) Infinite Potential Well Imagine that the “box” is a region with $0$ potential energy, and everywhere outside ...
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17 votes

Does the "particle in a box" necessarily form a standing wave?

The particle in a box does not necessarily form a standing wave. In fact in quantum mechanics these are states of definite energy that have trivial time evolution, but superpositions of them have non-...
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0 votes

Wind and sound waves

The curving pattern is not the only difference between (a) and (c). Look at the density of the rays coming from the source. In (a), it shows that the leftward wind would create a higher density of ...
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1 vote
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Generalization of spherical waves for arbitrary number of dimensions

If we assume time-harmonic signals, then we may write (as @Prahar suggests) $$\psi(r,t)=e^{-i\omega t}f(r).$$ Substituting this into the $N$D wave equation yields the $N$D Helmholtz equation: $$f'' + \...
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0 votes

Two waves of frequencies 2kHz and 2.1kHz are traveling in the same direction. Will they produce beats?

If you combine (for example by applying them to the same detector) two waves with different frequencies, they will produce beats. Noise is a random variation of a signal variable. If your two waves ...
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1 vote

Does a tower bell ringing prevent thunderstorms?

The energy scale of thunderstorm is much larger than that of a bell (most other devices built by humans), so it is unlikely that such devices can affect thunderstorms in a controllable way. A single ...
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0 votes

How to solve the Helmholtz equation in damped oscillator BCs?

Short answer: Replace $\omega$ with $\omega-i\xi$. Longer Answer: The Helmholtz equation is derived from the wave equation, which may be written as $$\nabla^2P -\frac{1}{c^2}\frac{\partial^2P}{\...
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2 votes

Sound waves adding up

You can compare this to taking the mean of a random sample of mean zero random variables. Some observations will be positive, and some will be negative, and so there will be a lot of canceling. ...
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0 votes

How to Model Chirp in Laser Pulse

Firstly, in your code you are confusing wavelength with frequency. You defined $\omega_0$ as 1µm. That is a typical wavelength ($\lambda$). $\omega=\frac{2\pi c}{\lambda}$ For 1µm wavelengths you need ...
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0 votes
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Can the dynamic between high speed sound media and slow one preduce shock wave?

Yes- sort of. High-speed movies of nuclear explosions near the ground show that the shock wave travels faster in earth than in air. The disturbed earth then begins to propagate an acoustic pulse up ...
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13 votes

Sound waves adding up

Since the phases are random, the waves do not add coherently... but neither do they cancel coherently. Furthermore, loudness is really a measure of the intensity of the sound. Thus, if we consider a ...
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0 votes

The 1D wave equation with gravity and the catenary

See Time Independent and Time Dependent Catenary Problem, a short paper that includes diagrams and derivations and behind some of what probably_someone posted.
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1 vote

Maximum oscilations of air molecules

What you are most likely referring to is an acoustic standing wave, and asking whether the air molecule velocity is highest at pressure nodes. The short answer to this is, yes, the air molecule ...
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4 votes
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Is there an electromagnetic analogue of thermoacoustics?

Yes, you are describing a waveguide which is a pipe that is used to conduct microwaves. It is possible to build standing electromagnetic waves inside such a pipe, giving rise to the klystron and ...
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2 votes
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Why the amplitude of monopole solution in Helmholtz equation is complex?

If there is a single monopole it does not matter whether $A$ is real or not but if you have two or more sources then their relative phases, and thus the phase of $A$, do matter. The same holds if the ...
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3 votes
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Resonant cavity for sound waves

The equation for the resonant frequencies are correct. To get to that equation you indeed need to impose the boundary conditions such that at the boundaries the wave vanishes, which is at $x=y=z=0$, $...
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1 vote

Can two waves have the same amplitude but different frequencies?

Ofcourse they can. What makes you think that they can't? High frequency waves do not necessarily have more energy than lower frequency waves also. $f = A\cos(\omega_{1} t)$ $f= Acos(\omega_{2} t)$ ...
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2 votes
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How can we derive an equation for double slit interference without the approximations made?

For near-field effects, it may be better to think about the full field rather than just path differences. Based on you wording of "point sources" and the fact that you are using speakers, I ...
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0 votes

What formalism is used to model thin film optical coatings that function across a range of angles of incident light?

Typically thin film design is done on a computer. The design would use a number of specific wavelengths. Sometimes you only need those specific wavelengths. E.G. you want the film to be transparent to ...
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0 votes

How do we get from LHP to RCP on the poincare sphere?

I don't quite understand the geometry proposed by the author but consider the following: The left-handed and right handed circular light are described by the Jones vector \begin{align} \vert LHP\...
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1 vote

Phase difference and path difference relation confusion

$\delta$ is the phase-difference $\theta_2 - \theta_1$ at the meeting point, where $\Delta x$ is the path-difference (difference in path lengths) $\ell_2 - \ell_1$ between the two paths from the ...
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0 votes

Wave without trough?

Definitely what you can see there exists. It is an image of a real experiment on solitons in fluids. I think that most people will call it a wave. However, the equation satisfied by such a wave or ...
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  • 6,568
-3 votes

Wave without trough?

A wave has both crest and trough (undulating form) portions of the same amplitude and frequency. A wave with zero amplitude and zero frequency i.e. a monochromatic infinite straight line (if we are ...
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2 votes

How to predict the time domain of pulse from an amplitude mask in frequency domain?

First of all, I think the OP has some misconceptions, so I will start by addressing them "These pulses often contain multiple frequencies (i.e. polychromatic pulse) that are generated by pulse ...
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1 vote

Nomenclature for stationary states in the context of wave equations

There is no universal standard for naming those solutions. For mechanical or electromagnetic waves, a stationary wave is a wave that doesn't travel, typically of the form: $$s(x,t)=A\cos(kx)\cos(\...
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0 votes
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How do we determine refractive index of a photonic crystal?

Setup In this answer we'll use a concrete model as an illustration. It doesn't limit the generality of this discussion, but (hopefully) helps understanding. In particular, we'll have a $z$-homogeneous ...
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1 vote
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What does quadrature mean in the context of sine waves and resonance?

Consider a signal $s(t)$ which oscillates at a frequency $f$. In general, such a signal will look like a sine wave offset by an arbitrary phase $\phi$ \begin{equation} s(t) = A \sin(2\pi f t + \phi) \...
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2 votes
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Why is skin depth quoted as when the amplitude has decayed by a factor of $\frac{1}{e}$

The mathematics (exponential decay) would suggest that infinite distance is needed for the amplitude to decay to zero. This would not be helpful, so an arbitrary agreed value is used. The choice of 1/...
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4 votes

Why is skin depth quoted as when the amplitude has decayed by a factor of $\frac{1}{e}$

Because the decay of an electromagnetic wave is exponential, i.e. it decays as $A_0e^{-z/\delta}$, where $A_0$ is the initial amplitude, $z$ is the distance in the conductor, and $\delta$ is the skin ...
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5 votes

Transverse waves in a rope: Why does tension not increase?

Due to the disturbance the tension in the rope will increase from $T$ to $T+\delta T$ where $\delta T \ll T$ due to the elastic properties of the rope. If the rope makes some small angle $\delta \...
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0 votes

Transverse waves in a rope: Why does tension not increase?

First of all, you cannot increase tension on a rope by stretching it without this having any elasticity. So elasticity of the material is necessary to increase tension. Increase in one dimensional ...
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10 votes
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Transverse waves in a rope: Why does tension not increase?

The short answer is that the elasticity does affect the wave speed. However, when people typically talk about the wave speed on a taut string they are referring to very small disturbances. In the ...
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2 votes

Why solid makes sound upon hitting?

Here is a simplified answer. Let's say you strike a piece of wood with a hammer. The hammer possesses kinetic energy and momentum and some or all of these will be transferred to the wood, a process ...
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2 votes

Green's function in 3+1D Minkowski spacetime

In order to make the Green's function unique, you need to specify a boundary condition. For the boundary condition $\lim_{t\to -\infty}G(\mathbf{x},t)=0$ (which is probably the most often used one) ...
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0 votes

Standing Wave Equation: Why does assuming a small slope $du/dx$ not make $d^2u/dx^2$ negligible as well?

The two entities, du/dx and d/dx(du/dx), don't have the same units. That means they cannot be compared. If one is 'small' in some sense, the other need not be. That second derivative, with the ...
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0 votes

Standing Wave Equation: Why does assuming a small slope $du/dx$ not make $d^2u/dx^2$ negligible as well?

From my own experience in the past, there is a common beginner's mistake in interpreting notation. It makes a big difference if $du/dx(x_0)=0$ for a single location $x_0$ or $du/dx(x)=0$ for all $x$ ...
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-1 votes

Why solid makes sound upon hitting?

You ask: why it vibrates? what happens in the quantum level? I will quote from this book's chapter abstract to see how complicated the answer is: Optical Properties of Ions in Solids pp 107–...
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0 votes

Standing Wave Equation: Why does assuming a small slope $du/dx$ not make $d^2u/dx^2$ negligible as well?

In the video, he is not assuming $\frac{du}{dx}$ is small. It has a definite nonzero value. He is taking the limit as $\Delta x$ gets small (goes to zero, or becomes an infinitesimal $dx$). That ...
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3 votes

Standing Wave Equation: Why does assuming a small slope $du/dx$ not make $d^2u/dx^2$ negligible as well?

Let's take an example signal: $y=\cos(x)$ about $x=0$. $\frac{dy}{dx}=-\sin(0)=0$; $\frac{d^2y}{dx^2}=-\cos(0)=-1$. It is important to note that one is not simply the square of the other.
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1 vote
Accepted

How can I show that applying Hamiltonian dynamics recovers the original wave equation?

$$ \frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2}\tag{1}$$ with $ u = u(t, x)$ over domain $x \in [0, l] = \Omega$. This can be represented as a Hamiltonian system with ...
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