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36

An animation is worth a million words:


26

It does, but the effects are negligible in the regions we think about. If you think about a volume of air as a box of atoms bouncing around, you can apply an oscillating pressure gradient across that box and show that it behaves close enough to an ideal wave propagation medium that you can get away with using such an ideal model. The variations you are ...


18

In this case it's probably best to be pragmatic. A pulse can be described as a superposition of sine waves that extend infinitely into space and time. But it's just that: a mathematical description that is useful for your purposes. There is not necessarily a physical meaning connected to it. Nevertheless, in quantum mechanics the wave-description of ...


16

They do, its just usually negligible in practice. There's also scattering because the particles are not all the same (H2O, N2, O2, etc.)--but that, too, is usually negligible. Its mainly because there are so many particles in a single wave. Consider that the wave must be extremely short before it becomes noticeable (megahertz).


11

This will be a purely mathematical treatment. It needs to be combined with some practical playing around to really "get" it. Traveling wave Let's start with the description of a harmonic traveling wave in one-dimension. Here "harmonic" just means the mathematical form of the wave is sinusiodal in both time and space. For concreteness we'll using talk ...


6

Dispersion in waves arises from both material property variation with frequency and from the geometry of the fields in question. That wave dispersion will arise from material property variation is obvious. But wave geometry and boundary conditions also matter. Simple example: a conductive waveguide with rectangular cross-section with sidelengths $a$ and $b$...


6

I just wanted to add to a previous (very accurate) answer: you can think of it as an Fourier expansion of the actual (physical) wave profile. It is not a real life process, it is a mathematical approximation. The wave pulse can be thought of as a superposition of plane waves, which happens to interfere destructively in entire space, except for the localized ...


6

My high school physics teacher was saying that “this is because of interference of sound waves. During the day, there are a lot of sounds and they cancel each other due to interference. But, during the night, there are few sounds and they can reach to our ears without canceling each other”. You need a better high school physics teacher. Temperatures tend ...


6

Any physical phenomenon is potentially capable to cause some change to any other phenomenon, more or less directly. If it was not the case, the physical world could be divided into completely independent realms; there would not be the one single world we call Nature. Practically though, many if not most of the actually existing interactions between systems ...


5

I can answer half your question in that a sound can change the path of light. A change in the density of the air produces a change in the refractive index of the air and so a Schlieren photograph can make this visible. Here is a YouTube video to show a sound wave produced by clapping.


5

how is a standing wave related to the atomic orbit (It is my understanding that the atomic orbit is both a mathematical function that describes the probability of an electron being at a certain place, but it is also the image of this function in terms of real space, i.e. the actual 3 dimensional volume around the nucleus that a particular electron calls "...


4

Imagine something oscillating in space and time, for example a plane wave propagating across the axis $x$. This propagation is expressed via the so-called phase $$ \phi(x,t)=\omega \cdot t - k\cdot x = \dfrac{2\pi}{T}\cdot t -\dfrac{2\pi}{\lambda}\cdot x \tag{01} $$ and the magnitude of the plane wave as $$ E(x,t)=A\cos\phi(x,t) \tag{02} $$ As the ...


4

This is a lot more subtle problem than is indicated in any of the comments. The problem is not just the issue of how the sum of non-causal signals can approximate a causal one, but how is it possible that while all real-life signals must start and stop at some time they must also be band-limited beyond some frequency, but as we know these two are ...


4

The battery on your smart phone only provides approximately 3 W of power to the phone's transmitter. This is enough power to reach a nearby cell tower, but totally insufficient to send a signal for several hundred miles. Due to this, the nearest cell tower is used to relay your signal to another cell tower that is located close to the party that you are ...


4

Do radio waves from the Sun reach Earth? Of course they do. It's just another form of electromagnetic radiation. If so, do they penetrate the atmosphere or are they reflected, absorbed, or scattered? That depends on frequency (or wavelength). The atmosphere reflects, absorbs, or scatters most incoming electromagnetic radiation. There's a window in ...


3

The photon is an elementary particle in the standard model of particle physics. It does not have a wavelength. It is characterized in the table as a point particle with mass zero and spin one. Its energy is given by E=h*nu, where nu is the frequency of the classical electromagnetic wave which can be built up by photons of the same energy. This is where ...


3

The maximum and minimum are "local" values. As you move closer to A (at 0.2 m you are MUCH closer to A than to B) the amplitude of A is much larger - so although there may be destructive interference between A and B at that point, this is by no means perfect interference, and the resulting amplitude is still quite large (lot of A minus a little of B). ...


3

In this type of problem one has to take great care in defining intensities. In this case there are 4 different intensities: 1. $I_{ss}$, the intensity received by the static observer as perceived by himself, 2. $I_{ms}$, the intensity received by the moving observer as perceived by a static observer. 3 $I_sm$, the intensity received by the static observer as ...


3

I would tend to agree that background noise is a factor, but rather than reducing, adding to the sound you are trying to make sense of. So part of that may be how your brain is able to filter the information from the background noise. But at night the temperature is lower and according to this tutorial on sound propagation (which does cite reliable ...


2

To add to the existing answer, I think there is a nomenclature issue. When you say "bass" people understand "low frequencies" but what you probably mean is "beat". Rapid changes in amplitude, like a beat, carry a lot of high frequencies. You do hear mostly the beat from other peoples' headphones, ans it's annoying. You can think about the extreme case: the ...


2

Yes, sound waves in a gas, liquid or solid can affect the light passing through it, as the motion of the atoms due to sound waves changes the atomic spacing, and this changes the index of refraction slightly. So the light would be diffracted and some amount of the light would experience a frequency shift up and a frequency shift down by the sound wave ...


2

I'd like to add to ACuriousMind's Answer. His/Her answer emphasizes that Maxwell's equations and other equations that give rise to the Huygens spherical wave kernel in their Green's functions are inherently acausal and we must force causality by hand through the appropriate boundary conditions. In antenna problems, we simply discard the advanced wave part ...


2

Basically it is whatever you need to multiply a distance by to find a phase difference (in radians). For a traveling wave, the wave number is the amount of phase difference per unit length. For a physical sine wave, it is the ratio between the maximal slope of the wave surface and the amplitude. In other words, it measures how dramatic the local ...


2

The Poynting vector is just an intensity vector, it is just $\vec S = \vec E \times \vec B$, one might need some factors of $c$ in there, I have been in $c = 1$ land too long …. Due to the time dependence, the amplitudes of the electric fields are time dependent. If one would call that flickering, it would be the frequency of the light. I don't think that ...


2

You have the correct conclusion, and I think you have the correct analysis, but I don't fully understand your presentation. Think of it this way: If the displacement occurs only between "neutral" and "forward", then the average density (air molecules per volume, or spring coils per length) over the entire system (air chamber or spring) must increase. But ...


2

In general, a mixed wave of the form $$ f(x,t)=\cos(x-t)+r\cos(x+t) $$ will not have nodes, at least in the sense of points $x_0$ for which $f(x_0,t)\equiv 0$ for all times $t$. In general, there's relatively little to say beyond what the picture will convey: As you turn $r$ up from 0 to 1, you first start inducing modulations into the amplitude of the ...


2

He is referring to the second paragraph of 31-3: However, we shall discuss the formula we have obtained, in various possible circumstances. First of all, for most ordinary gases (for instance, for air, most colorless gases, hydrogen, helium, and so on) the natural frequencies of the electron oscillators correspond to ultraviolet light. These ...


2

My theory is that since water, and indeed all liquids, are incompressible, they both form at the same time. As the pebble hits the surface of the water and pushes it down, the surrounding liquid is pushed up (relative to the original surface level of the liquid), as you stated. Any displacement of a liquid must be accounted for.


2

The D'Alembert solution has a simple interpretation. Using your notation, it reads $$\phi(x, t) = \frac{g(x-t) + g(x+t)}{2} + \frac12 \int_{x-t}^{x+t} h(x') dx'.$$ where $g(x)$ is the initial position, $h(x)$ is the initial velocity, and $v = 1$. The intuition is as follows: the first term above solves the wave equation with initial position $g(x)$ but zero ...


2

A standing wave is basically two opposing waves of equal amplitude, as shown in the diagram below (where n is a positive integer): You can see this more clearly if you look at the top line where n=3, and follow it as it goes down, up, down. That's wave one. Then, if you look at the bottom line in the same case as it goes up, down, up, that is the opposing ...



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