# Tag Info

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When the source is vibrating in a simple harmonic manner in a particular direction, how can spherical wavefronts be produced? Most speakers cannot produce much directionality to the sounds that come from them. They are so small compared to the wavelengths produced that diffraction effects are very large. Directionality comes more from the cabinet or ...

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The sinusoidal shape of a wave on water or on a string represents a spatial displacement- the actual movement of the surface of the water or the position of the string. `The sinusoidal representation of an electromagnetic wave doesn't represent a spatial displacement at all, so you must not think of it as being directly comparable to the water wave in that ...

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In the reference of waves, disturbance is a change in a certain quantity pertaining to that wave. Like in the sound waves, the disturbance is the pressure or density variation at a point. In the case of a string wave, the disturbance is in the amplitude of a point on the string at different times. A wave carries energy with it thus, a wave can transfer ...

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Think about an array of dominos. The first knock the second, which in turn knocks the third, and so on... In this metaphor, the disturbance is the tilting of the dominos (the energy they temporarily acquire and release in the successive collisions). In the metaphor above, energy travels as the successive domino fall. Only one domino at the time is in ...

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The resonant frequencies are determined by an object's geometry, material composition, and the boundary conditions placed on the object. Unless the object is self aware it cannot do anything to itself. However, if some of the above properties change in time then, YES, the resonant frequencies will change too. This is an observed phenomenon in musical ...

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Without the random movement of molecules, it is true that a vibrating membrane for example would create a depleted region around. It is like a fight in the middle of a crowd. Suddenly there is a clear region around the event and a wave of pressure that extends for some distance. But because of that random movements, any depleted area is filled almost ...

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Sound waves are referred to as pressure waves, and if you understand this, it should answer your question. When sound waves propagate, they form alternate regions of high pressure, called compressions, and low pressure, called rarefactions in the air. The air molecules move toward and away from these regions as the wave propagates. It is not that momentum is ...

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Your question is a question on elastic collisions, disguised as a question on wave mechanics: What I don’t understand is how the air molecules move back to approximately their original position after colliding with the other particles to keep the wave moving further. Doesn’t this seemingly violate the laws of conservation of momentum? The fact that, after ...

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Audio speakers are, in general, not particularly directional. That is to say, the sound emitted from the speaker spreads out in all directions. With the exception of ultrasound frequencies, it is impossible to 'beam' sound energy along a narrow path with a speaker of practical dimensions. This is due to the relative size of sound-waves and speakers. A normal ...

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Yes, there should be a time delay that could be measured experimentally. A good way would be to use a long U shaped tube and measure the length as accurately as possible. Film the experiment with high speed film that does a certain number of frames per second. Drop a weight onto the liquid, that covers most of the area at one end of the tube and by seeing ...

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Sound requires fluid dynamics, and fluid dynamics requires collisions between molecules so that he notion of a local pressure exerted by one bit of the gas on its neigbour makes sense. Once the size of the moving object becomes comparable to the mean-free-path of the gas molecules, fluid dynamics become inapplicable and a Mach number cannot be defined. ...

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Yes. For example, when you play a trumpet, you use the valve buttons to change the length and thereby the resonant frequency of the trumpet tube and thereby produce different resonant frequencies- and you can play different notes.

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As mentioned by @mikestone, you need two conditions for this problem. What I suspect is that you are solving for an infinite domain and might obtain solutions that are proportional to $1/r^n$. These terms are unbounded in the origin of the system and their constants are taken as zero for the solution to be physically admissible. If your domain does not ...

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The resonant frequency of an object depends on its internal stress distribution. For example, when you tune a guitar, you change the resonant frequency of the strings by changing their tension. The resonant frequency also depends on Young's Modulus, which changes with temperature for most materials.

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The wave equation is an hyberbolic partial differential equation. You need Cauchy Data (for example, initial value and time derivative of $p({\bf x},t)$ at time $t_0$) to determine the solution. Boundary data is what is needed for elliptic equations such as $\nabla^2\phi=0$. This is true independently of the chosen coordinate system.

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One way to look at it is the following : In theory, ideally, you could use one single speaker on your hi-fi, just the way it’s done on a cheap radio. However, you would face two problems if using one single speaker instead of a medium, plus a woofer plus a tweeter: Efficiency (bandwidth): When you send an electric signal of a given frequency f to a speaker,...

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subwoofers need to be bigger than tweeters because as the frequency is reduced, the radiation resistance of the speaker cone goes down because the cone impedance is mismatched relative to the air it is radiating into. To remedy this, the cone diameter needs to be increased for best efficiency at low frequencies. This "best diameter" scales more or ...

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While dealing with amplitude for a particular 𝑥, why are we considering only the first term, i.e, $\cos\left(\frac{\omega_1−\omega_2}{2}t\right)$? The amplitude is the product of the $\sin$ and $\cos$ terms. Since $\sin(x) \leq 1 \,\,\forall x$, the product of the two terms can never exceed $A\cos(\ldots)$. It will at most times be smaller, and oscillate ...

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The variables are related by the ideal gas equation $pV=nRT$. We can write $n = m/M$ where $m$ is the mass of the gas and $M$ is its molar mass. Therefore we have $$pV=nRT \\ pV=\frac{m}{M}RT \\ p = \frac{m}{V} \frac{RT}{M} = \frac{\rho RT}{M}$$ The equation for speed can also be written as $$v = \sqrt{\frac{\gamma RT}{M}}$$ Your statements depend on what ...

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What most people call speed of sound in solids is the following $$c = \sqrt{\frac{E}{\rho}}\,$$ that is speed of a wave propagating in a slender bar. This value is between the speed of shear and longitudinal waves. You normally don't find these values with uncertainties because they are used as reference values. In an application that requires a precision ...

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First, the size of the air cavity affects the low frequency of the guitar (see this answer), but the most important part for mid and high frequencies is the top plate, and its interaction with the resonant air. The air enclosed in your air cavity works as a Helmholtz resonator, which frequency is given by $$f = \frac{v}{2\pi}\sqrt{\frac{A}{V L_{eq}}}\, ,$$ ...

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Subluminal warp bubbles have a surface, and it is made of some physical material 1. If such objects were to interact with the atmosphere, the usual intuition applies regarding how solid objects interact with gases. Subluminal and subsonic warp drives don't make sonic booms, and subluminal supersonic warp drives do make sonic booms, just like any other ...

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Here are some general considerations. Noise control requires prevention of transmission through the walls and the provision of absorption inside the walled room. Unfortunately, bass frequencies penetrate ordinary walls readily and are the hardest frequencies to absorb inside the walls of a room. Killing off the bass transmission through the walls requires ...

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If you really want to maximise the volume, explain this to the other residents. Ask them join the test - to listen and to tell you if they can hear it. But remember, what might seem quiet to them in the daytime might seem loud if they are trying to sleep. So if they agree something, go for quieter than they agreed. Then you can enjoy the party with a ...

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You have chosen a very complicated system to analyze. In general: increasing the box volume decreases its resonant frequency, and matching the string frequency to the box frequency will decrease the sustain time. Writing an equation expressing this is a term project task for an upper division engineering student.

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You are correct, the angle of the transmitted beam depends on the order of diffraction and the frequency shifted. The effect can be significant, for example, we use AOMs in our lab to shift the frequency of a beam to image $^{87}$Rb atoms, we see a sudden drop in intensity after some change in frequency due to the shifted beam not coupling into the fiber ...

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In the building example, you are following the stone on its parabolic trajectory for all time. The negative time solution is the 1st time it crosses $h=0$, reaching the top of the cliff at $t=0$, and then falling as per the problem. Onto the stone and the well: If the stone fall a distance $x$ in time $t_0$, then the sound is heard at: $$t_1 = \frac x c + ... 0 So, first: As waves travel trough the fluid and scatter on impact with a particle, the particle gets pushed away. This acting force is called acoustic radiation force (ARF), and was first described by King in 1934. Some years later Gor'kov revised the formula and said, that this force is (like) a potential force U and therefore also called Gor'kov potental. ... 1 Some problems come down to algebra. In your equation after (3), multiply and divide by \rho (under the square root), combine the \rho in numerator, then substitute P for K\rho^\gamma. That gives \gamma P/\rho. Ideal gas law is P=\rho R_g T where R_g is the gas constant for the gas, e.g., R=8.314 J/K mol, 1 mole of air is about .o29 kg, so R_g=8.... 2 The speed of sound does indeed depend on the amplitude/loudness/excitation force. However, for sufficiently weak waves, and if we ignore a variety of additional effects (such as drag and internal friction), we can approximate the speed of sound as constant. The intuitive reason is that any smooth minimum in a curve looks like a parabola up close. I'll ... 8 I think this is indeed a very interesting question. When I first read the answer by endolith I thought that it was not right, because it is based on a very simple Rayleigh-Jeans estimate that goes back to a paper from 1933, published long before Landau and Lifshitz developed the modern theory of fluctuations in fluid dynamics (1957, described in vol II of ... 0 Sound in air is a periodic variation in pressure that propagates with a characteristic speed. When the frequency and amplitude of the variation is sufficient to vibrate the mechanism within your ear, you will hear it. There is no hard minimum frequency for periodic variations in air pressure, although as the frequency becomes very low (much less than 1Hz) in ... 2 First of all, it depends on the size and shape of the plate. As a rule of thumb, the wave length cannot be longer than two times the extent of the object, which gives us the rough estmate of frequency as$$f=\frac{v_{sound}}{\lambda} A more precise answer requires finding the eigenmodes of the plate (i.e., solving the sound wave equation with the boundary ...

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